738:
713:
3184:
730:
32:
77:
6163:
5503:), except for that a full circle doesn't equal 360 degree, 6.2831... rad or 400 gon, but 1 turn. (I found it to be really convenient in engineering/programming, where you often have to convert to/from other unit representations But I think it can also be useful for educational purposes. ) Having the angle of a full circle normalized to 1 allows for easier
2895:
452:) and corresponding to one turn, for greater conceptual simplicity when stating angles in radians. This proposal did not initially gain widespread acceptance in the mathematical community, but the constant has become more widespread, having been added to several major programming languages and calculators.
4685:
The following table documents various programming languages that have implemented the circle constant for converting between turns and radians. All of the languages below support the name "Tau" in some casing, but
Processing also supports "TWO_PI" and Raku also supports the symbol "τ" for accessing
2999:
5966:
2780:
5361:"Richtlinie 2009/3/EG des Europäischen Parlaments und des Rates vom 11. März 2009 zur Änderung der Richtlinie 80/181/EWG des Rates zur Angleichung der Rechtsvorschriften der Mitgliedstaaten über die Einheiten im Messwesen (Text von Bedeutung für den EWR)"
6535:[from which it is clear that the point B is pushed by a given distance from its natural position, and it will reach the maximum distance after the elapsed time t=π/m, π denoting an angle of 180°, which becomes cos(mt)=- 1 & B b=2α.]
2418:
2320:
2618:
2544:
716:
An arc of a circle with the same length as the radius of that circle corresponds to an angle of 1 radian. A full circle corresponds to a full turn, or approximately 6.28 radians, which is expressed here using the Greek letter
2762:
2696:
6158:{\displaystyle {\overline {{\tfrac {16}{5}}-{\tfrac {4}{239}}}}-{\tfrac {1}{3}}{\overline {{\tfrac {16}{5^{3}}}-{\tfrac {4}{239^{3}}}}}+{\tfrac {1}{5}}{\overline {{\tfrac {16}{5^{5}}}-{\tfrac {4}{239^{5}}}}}-,\,\&c.=}
2901:
1862:
1810:
4480:
6733:; Chen, Hongyu; Aylward, Graeme; Jorritsma, Megan; Mann, Christina; Defaz Poveda, Diego David; Pierce, Cayden; Lam, Derek; Stairs, Jeremy; Hermandez, Jesse; Li, Qiushi; Xiang, Yi Xin; Kanaan, Georges (June 2019).
1469:
1038:, 𐤈 or ט, and it has been observed that the older version of the symbol, which means wheel, resembles a wheel with four spokes. It has also been proposed to use the wheel symbol, teth, to represent the value 2
1432:
1705:
2182:
2032:
5336:"Richtlinie 80/181/EWG - Richtlinie des Rates vom 20. Dezember 1979 zur Angleichung der Rechtsvorschriften der Mitgliedstaaten über die Einheiten im Meßwesen und zur Aufhebung der Richtlinie 71/354/EWG"
4558:
4395:
6533:
unde constat punctum B per datum tantum spatium de loco fuo naturali depelli, ad quam maximam distantiam pertinget, elapso tempore t=π/m denotante π angulum 180°, quo fit cos(mt)=- 1 & B b=2α.
3169:
3135:
3079:
3045:
2108:
1955:
2890:{\displaystyle e^{{\color {orangered}2\pi }i{\frac {k}{n}}}=\cos {\frac {{\color {orangered}2}k{\color {orangered}\pi }}{n}}+i\sin {\frac {{\color {orangered}2}k{\color {orangered}\pi }}{n}}}
1654:
1583:
1549:
1042:, and more recently a connection has been made among other ancient cultures on the existence of a wheel, sun, circle, or disk symbol—i.e. other variations of teth—as representation for 2
942:, which amounts to the number of radians in half a turn, in order to make mathematics simpler and more intuitive. His proposal used a "π with three legs" symbol to denote the constant (
977:
5499:
I'd like to see a TURN mode being implemented as well. TURN mode works exactly like DEG, RAD and GRAD (including having a full set of angle unit conversion functions like on the
4982:
6427:
Leonhardi Euleri opera omnia. 1, Opera mathematica. Volumen VIII, Leonhardi Euleri introductio in analysin infinitorum. Tomus primus / ediderunt Adolf Krazer et
Ferdinand Rudio
1021:
2326:
2225:
2439:
2550:
2473:
450:
415:
380:
781:
5364:
5781:
2702:
2633:
2459:
5339:
5457:
5757:
7492:
6891:
633:
While percentage protractors have existed since 1922, the terms centiturns, milliturns and microturns were introduced much later by the
British astronomer
5588:
7380:
5539:
5254:
2994:{\displaystyle e^{{\color {orangered}\tau }i{\frac {k}{n}}}=\cos {\frac {k{\color {orangered}\tau }}{n}}+i\sin {\frac {k{\color {orangered}\tau }}{n}}}
6859:
6949:
4423:, resulting from a ratio of angular displacement. It can be negative and also greater than 1 in modulus. The relationship between quantity rotation,
1067:. He offered several reasons for the choice of constant, primarily that it allows fractions of a turn to be expressed more directly: for instance, a
6400:
6456:
5724:
5176:
4755:
7481:
7424:
7120:
6882:"Let's Use Tau--It's Easier Than Pi - A growing movement argues that killing pi would make mathematics simpler, easier and even more beautiful"
1816:
1761:
6180:(among others for the same purpose, and drawn from the same Principle) I receiv'd from the Excellent Analyst, and my much Esteem'd Friend Mr.
5039:"Measurement units of quantities of dimension one are numbers. In some cases, these measurement units are given special names, e.g. radian..."
4433:
1196:(which Hartl also calls "Euler's identity") is more fundamental and meaningful. He also claims that the formula for circular area in terms of
6290:
7324:
511:
5397:
6224:
1438:
6266:
5937:
5933:
5927:
5487:
1401:
5427:
501:
6317:. Bullettino di Bibliografia e di Storia delle Scienze Matematiche e Fisiche (in French). Vol. 19 (published 1886). p. 139.
5212:
4351:
is the number (not necessarily an integer) of revolutions, for example, of a rotating body about a given axis. Its value is given by:
7398:
5119:
5115:
681: turn. The binary degree is used in computing so that an angle can be represented to the maximum possible precision in a single
1660:
1249:
Initially, this proposal did not receive significant acceptance by the mathematical and scientific communities. However, the use of
6663:"Trig rerigged. Trigonometry reconsidered. Measuring angles in 'unit meter around' and using the unit radius functions Xur and Yur"
5722:
Croxton, Frederick E. (1922). "A Percentage
Protractor - Designed for Use in the Construction of Circle Charts or "Pie Diagrams"".
2113:
1960:
4773:
5895:
5012:
The angular unit terms "cycles" and "revolutions" are also used, ambiguously, as shorter versions of the related frequency units.
903:, sometimes for 3.14... and other times for 6.28..., became widespread, with the definition varying as late as 1761; afterward,
6662:
5837:
5250:
Handbuch SI-Einheiten: Definition, Realisierung, Bewahrung und
Weitergabe der SI-Einheiten, Grundlagen der Präzisionsmeßtechnik
6435:
4516:
4357:
7461:
5672:
The
Science of Measurement: A Historical Survey (The World of Measurements: Masterpieces, Mysteries and Muddles of Metrology)
5084:
86:
about the center point starting from the right, where a complete rotation corresponds to an angle of rotation of 1 turn.
5907:
5841:
5691:
5632:
5582:
5533:
5312:
5266:
7008:
6920:
882:
3141:
3104:
7196:
7062:
6979:
6723:
5360:
4791:
4323:
3051:
3014:
2039:
1886:
456:
6782:
6611:
1619:
1289:
41:
5335:
938:
In 2001, Robert Palais proposed using the number of radians in a turn as the fundamental circle constant instead of
7033:
5449:
1555:
1518:
459:, an arbitrary "number of turns" (also known as "number of revolutions" or "number of cycles") is formalized as a
7091:
5766:
7141:
1343:
7580:
6881:
6582:
5801:
4732:
4706:
7349:
5569:
5152:
5030:"The special name revolution, symbol r, for this unit is widely used in specifications on rotating machines."
945:
7575:
5923:
4993:
4844:
4750:
4413:
1281:
852:
784:
551:
support the unit symbol "tr" for turns since 2011 and 2013, respectively. Support for "tr" was also added to
7235:
7159:
6847:
5872:
5520:
2466:
2218:
20:
6941:
986:
proposed the idea of defining a constant as the ratio of circumference to radius, a proposal supported by
6397:
5504:
4882:
4862:
4786:
2626:
1309:
1297:
1285:
4900:
4804:
4309:
1293:
644:
5479:
5186:
7448:
6526:
5683:
5419:
5393:
4420:
532:
7112:
4887:
5675:
4671:: rotation and angle, respectively. "Cycle" is also mentioned in ISO 80000-3, in the definition of
2413:{\displaystyle f(a)={\frac {1}{{\color {orangered}\tau }i}}\oint _{\gamma }{\frac {f(z)}{z-a}}\,dz}
2315:{\displaystyle f(a)={\frac {1}{{\color {orangered}2\pi }i}}\oint _{\gamma }{\frac {f(z)}{z-a}}\,dz}
619:
4905:
4768:
1301:
6287:
6201:
4737:
4664:
4643:
4401:
3089:
997:
7317:
5899:
4719:
4491:
4945:
4715:
4585:
2613:{\displaystyle \varphi (x)={\frac {1}{\sqrt {\color {orangered}\tau }}}e^{-{\frac {x^{2}}{2}}}}
2539:{\displaystyle \varphi (x)={\frac {1}{\sqrt {\color {orangered}2\pi }}}e^{-{\frac {x^{2}}{2}}}}
460:
328:
7531:
7436:
6471:
6374:
6312:
6232:
5752:
5667:
5385:
5248:
5070:
7271:
Harremoës, Peter (2017). "Bounds on tail probabilities for negative binomial distributions".
6730:
6697:; Janzen, Ryan E.; Ali, Mir Adnan; Scourboutakos, Pete; Guleria, Nitin (22–24 October 2014).
6694:
6247:
2424:
648:
6817:
4499:
1870:
432:
400:
362:
333:
7478:"The NIST Guide for the Use of the International System of Units, Special Publication 811"
5890:
The Words of
Mathematics: An Etymological Dictionary of Mathematical Terms Used in English
5106:
2757:{\displaystyle n!\sim {\sqrt {{\color {orangered}\tau }n}}\left({\frac {n}{e}}\right)^{n}}
2691:{\displaystyle n!\sim {\sqrt {{\color {orangered}2\pi }n}}\left({\frac {n}{e}}\right)^{n}}
847:
on its own with its present meaning (of perimeter divided by diameter) was in 1706 by the
766:
8:
7590:
6886:
6699:"Integral Kinematics (Time-Integrals of Distance, Energy, etc.) and Integral Kinesiology"
5833:
5679:
5218:
4955:
4603:
1180:
685:. Other measures of angle used in computing may be based on dividing one whole turn into
6821:
6473:
Cursus
Mathematicus: Elementorum Analyseos Infinitorum Elementorum Analyseos Infinitorvm
5786:. History of the Smithsonian Satellite-tracking Program. Cambridge, Massachusetts, USA:
843:(delta over pi) for the ratio of the diameter to perimeter. The first use of the symbol
7372:
7298:
7280:
7000:
6775:
6750:
6706:
6603:
6450:
6348:
6195:
s Number, or that in Art. 64.38. may be Examin'd with all desireable Ease and
Dispatch.
6188:
5888:
4849:
4660:
4659:
The superseded version ISO 80000-3:2006 defined "revolution" as a special name for the
2444:
1305:
987:
899:
for one-fourth of the circumference of a unit circle, or 1.57... . Usage of the letter
638:
6829:
5386:"Art. 15 Einheiten in Form von nichtdezimalen Vielfachen oder Teilen von SI-Einheiten"
783:
was not originally fixed to the ratio of the circumference and the diameter. In 1697,
344:
of curves. Subdivisions of a turn include the half-turn and quarter-turn, spanning a
332:(rpm). The angular unit of the turn is useful in connection with, among other things,
7457:
7376:
7302:
6754:
6734:
6698:
6607:
5903:
5697:
5687:
5644:
5636:
5578:
5529:
5308:
5262:
5223:
5080:
5048:"3-14) period duration, period: duration (item 3‑9) of one cycle of a periodic event"
4940:
4579:
4564:
4337:
3097:
1319:
It has also been used in at least one mathematical research article, authored by the
322:
50:
46:
6669:
6497:
589:
7477:
7364:
7290:
6843:
6825:
6742:
6710:
6595:
6425:
6340:
5737:
5733:
5300:
4988:
4950:
4934:
4871:
4673:
4668:
1612:
1144:
983:
818:
4667:, these two specially named dimensionless units are applicable for non-comparable
4663:"one", which also received other special names, such as the radian. Despite their
4408:
The above definition is part of the ISQ, formalized in the international standard
7368:
6591:
6531:(in Latin). sumtibus Ambr. Haude & Jo. Carol. Speneri, bibliop. p. 200.
6404:
6294:
5866:
5296:
5292:
Das Vieweg
Einheiten-Lexikon: Formeln und Begriffe aus Physik, Chemie und Technik
5290:
5258:
5181:
3007:
1710:
353:
260:
257:
4867:
707:
7585:
7215:
6636:
6522:
6331:
Cajori, Florian (1913). "History of the Exponential and Logarithmic Concepts".
5787:
4831:
3264:
3238:
859:
858:
The first known usage of a single letter to denote the 6.28... constant was in
737:
345:
341:
281:
210:
7178:
6912:
6547:
6431:
6382:
6318:
6262:
5304:
5177:"Life of pi in no danger – Experts cold-shoulder campaign to replace with tau"
7569:
7294:
6808:
5862:
5625:
5227:
4976:
4314:
4280:
number of revolutions, number of cycles, number of turns, number of rotations
3188:
2770:
1050:
814:
753:
657:
516:
422:
394:
7054:
6971:
6746:
6574:
4827:
7253:
5648:
1588:
1260:
289:
7506:
7420:
6687:
4809:
4568:
317:
6182:
4959:
4925:
4409:
3192:
1857:{\displaystyle A={\frac {n}{2}}\sin {\frac {\color {orangered}\tau }{n}}}
1805:{\displaystyle A={\frac {n}{2}}\sin {\frac {\color {orangered}2\pi }{n}}}
1125: rad. As for the choice of notation, he offered two reasons. First,
991:
888:
349:
337:
253:
175:
101:
7456:(9th ed.), International Bureau of Weights and Measures, Dec 2022,
7029:
5605:
5556:
4475:{\displaystyle N={\frac {\varphi }{\text{tr}}}=\{\varphi \}_{\text{tr}}}
6599:
6381:(in Latin). Vol. 1. Academiae scientiarum Petropoli. p. 113.
6352:
5958:, which may very much facilitate the Practice; as for instance, in the
5674:. Dover Books on Mathematics (corrected reprint of original ed.).
5620:
4822:
4651:
4503:
1034:. The Greek letter theta derives from the Phoenician and Hebrew letter
634:
627:
623:
356:
can also be used as in, e.g., centiturns (ctr), milliturns (mtr), etc.
7142:"Constants @GDScript - Godot Engine (stable) documentation in English"
7083:
5603:
5554:
1167:
gives many examples of formulas that are asserted to be clearer where
6806:
Aron, Jacob (2011-01-08). "Michael Hartl: It's time to kill off pi".
5076:
4970:
1313:
1163:, whose association with the circle constant is unavoidable. Hartl's
1026:
The same year, Thomas Colignatus proposed the uppercase Greek letter
876:
810:
712:
651:, which implicitly have an angular separation of 1/32 turn. The
6344:
5812:
7558:
7285:
5577:. 0.12 (draft ed.). pp. iii, 54, 97, 128, 144, 193, 195.
4302:
1464:{\displaystyle {\color {orangered}{\frac {\tau }{4}}}{\text{ rad}}}
1243:
887:
though defined as half the circumference of a circle of radius 1—a
605:
564:
560:
548:
544:
83:
5148:
1427:{\displaystyle {\color {orangered}{\frac {\pi }{2}}}{\text{ rad}}}
891:—rather than the ratio of circumference to diameter. Elsewhere in
473:
of a given angle and a full turn. It is represented by the symbol
76:
4297:
3269:
3242:
1750:
647:
are also used. Sailors have traditionally divided a turn into 32
572:
568:
528:
285:
226:
7421:"ISO 80000-3:2019 Quantities and units — Part 3: Space and time"
5701:
5640:
696:
7220:
6379:
Mechanica sive motus scientia analytice exposita. (cum tabulis)
5500:
4983:
Divine Proportions: Rational Trigonometry to Universal Geometry
3259:
3234:
3196:
3183:
1277:
757:
580:
556:
552:
426:
277:
264:
141:
5809:
Manual & Technical Specifications - ooPIC Compiler Ver 6.0
5213:"For Math Fans, Nothing Can Spoil Pi Day—Except Maybe Tau Day"
4489:
is the numerical value of the angle 𝜑 in units of turns (see
1700:{\displaystyle A={\color {orangered}{\frac {1}{2}}\tau }r^{2}}
7532:"ISO 80000-1:2009(en) Quantities and units — Part 1: General"
5806:
5108:
Units & Symbols for Electrical & Electronic Engineers
4930:
4573:
2177:{\displaystyle S_{n}(r)={\color {orangered}\tau }rV_{n-1}(r)}
2027:{\displaystyle S_{n}(r)={\color {orangered}2\pi }rV_{n-1}(r)}
1327:
The following table shows how various identities appear when
1027:
848:
729:
615:
470:
6323:
Car, soit π la circonference d'un cercle, dout le rayon est
19:"360 degrees" and "360°" redirect here. For other uses, see
7402:
4710:
1035:
682:
7179:"JDK-8283136: Add constant for tau to Math and StrictMath"
6693:
6255:
Commentarii Academiae Scientiarum Imperialis Petropolitana
6855:
6739:
The 5th ACM Workshop on Wearable Systems and Applications
1054:
718:
504:(March 1974) proposed the unit symbol "pla" (from Latin:
418:
6729:
5378:
4553:{\displaystyle n={\frac {\mathrm {d} N}{\mathrm {d} t}}}
4390:{\displaystyle N={\frac {\varphi }{2\pi {\text{ rad}}}}}
741:
A comparison of angles expressed in degrees and radians.
6735:"Eye Itself as a Camera: Sensors, Integrity, and Trust"
6528:
Nova theoria lucis et colorum. Opuscula varii argumenti
6301:
is taken for the ratio of the radius to the periphery "
270:
6414:
denote the ratio of the diameter to the circumference"
6112:
6090:
6075:
6047:
6025:
6010:
5989:
5974:
733:
Some special angles in radians, stated in terms of 𝜏.
6430:(in Latin). Lipsae: B.G. Teubneri. pp. 133–134.
5969:
5758:
Astronomische Mitteilungen der Urania-Sternwarte Wien
4519:
4436:
4360:
3144:
3107:
3054:
3017:
2904:
2783:
2705:
2636:
2553:
2476:
2447:
2427:
2329:
2228:
2116:
2042:
1963:
1889:
1819:
1764:
1663:
1622:
1558:
1521:
1441:
1404:
1000:
948:
769:
435:
403:
365:
5528:. 0.12 (draft ed.). pp. 72, 118–119, 311.
1147:
637:
in 1962. Some measurement devices for artillery and
614:
milliturns, with each milliturn corresponding to an
7501:
7499:
7216:"Add Math.Tau Pull Request #37517 · dotnet/Runtime"
6361:
be the circumference (!) of a circle of unit radius
5255:
Friedrich Vieweg & Sohn Verlagsgesellschaft mbH
817:) divided by its radius. However, earlier in 1647,
583:
as well, but the calculator instead implements "MUL
7476:Thompson, Ambler; Taylor, Barry N. (2020-03-04) .
7415:
7413:
7411:
7152:
6157:
5887:
5624:
5211:
4552:
4474:
4389:
3164:{\displaystyle \omega ={\color {orangered}\tau }f}
3163:
3130:{\displaystyle \omega ={\color {orangered}2\pi }f}
3129:
3073:
3039:
2993:
2889:
2756:
2690:
2612:
2538:
2453:
2433:
2412:
2314:
2176:
2102:
2026:
1949:
1856:
1804:
1699:
1648:
1577:
1543:
1463:
1426:
1015:
971:
775:
444:
409:
374:
3074:{\displaystyle h={\color {orangered}\tau }\hbar }
3040:{\displaystyle h={\color {orangered}2\pi }\hbar }
2103:{\displaystyle V_{n}(r)={\frac {r}{n}}S_{n-1}(r)}
1950:{\displaystyle V_{n}(r)={\frac {r}{n}}S_{n-1}(r)}
956:
955:
954:
952:
910:Several people have independently proposed using
7567:
7496:
6873:
5879:
5811:. Savage Innovations, LLC. 2007 . Archived from
5171:
5169:
752:(approximately 6.28) is the ratio of a circle's
16:Unit of plane angle where a full circle equals 1
7408:
5826:
5725:Journal of the American Statistical Association
5205:
5203:
5062:
1649:{\displaystyle A={\color {orangered}\pi }r^{2}}
7482:National Institute of Standards and Technology
7469:
7425:International Organization for Standardization
7390:
7309:
7264:
6568:
6566:
6482:notet peripheriam circuli, cuius diameter eſt
6311:Euler, Leonhard (1747). Henry, Charles (ed.).
5744:
4506:of rotation with respect to time), denoted by
1263:began accepting answers expressed in terms of
5855:
5802:"ooPIC Programmer's Guide - Chapter 15: URCP"
5661:
5659:
5615:
5613:
5561:
5512:
5450:"Chapter 3: Units - Available Units - Angles"
5166:
4419:Rotation count or number of revolutions is a
1280:and in several programming languages such as
907:was standardized as being equal to 3.14... .
492:There are several unit symbols for the turn.
7441:
6552:(YouTube video). Information shown at 18:35
6248:"Tentamen explicationis phaenomenorum aeris"
5942:There are various other ways of finding the
5715:
5441:
5411:
5282:
5247:German, Sigmar; Drath, Peter (2013-03-13) .
5200:
5142:
5140:
4463:
4456:
1578:{\displaystyle C={\color {orangered}\tau }r}
1544:{\displaystyle C={\color {orangered}2\pi }r}
1276:is made available in the Google calculator,
1179:. For example, Hartl asserts that replacing
697:Proposals for a single letter to represent 2
626:divided in centiturns is normally called a "
522:
7524:
7341:
7228:
7160:"Get TAU - Unreal Engine 5.2 Documentation"
6963:
6905:
6879:
6836:
6563:
6455:: CS1 maint: numeric names: authors list (
6216:
5962:, the Diameter is to Circumference as 1 to
5885:
5794:
5507:to/from a whole bunch of other angle units
5295:(in German) (1 ed.). Vieweg, reprint:
5246:
5068:
4680:
4563:The SI unit of rotational frequency is the
4427:, and unit turns, tr, can be expressed as:
610:A turn can be divided in 100 centiturns or
505:
7047:
6993:
6880:Bartholomew, Randyn Charles (2014-06-25).
6767:
6546:sudgylacmoe; Hartl, Michael (2023-06-28).
6515:
6281:Sumatur pro ratione radii ad peripheriem,
5773:
5755:(ed.). "Bestimmung von Satellitenbahnen".
5656:
5610:
5240:
4498:In the ISQ/SI, rotation is used to derive
953:
75:
7315:
7284:
7270:
7246:
7189:
6799:
6661:Cool, Thomas "Colignatus" (2008-07-18) .
6654:
6142:
5838:"Angles, integers, and modulo arithmetic"
5750:
5471:
5137:
5116:Institution of Engineering and Technology
2403:
2305:
1255:has become more widespread. For example:
760:, and the number of radians in one turn.
7134:
5861:
5288:
5209:
3182:
972:{\displaystyle \pi \!\;\!\!\!\pi =2\pi }
736:
728:
711:
6969:
5896:The Mathematical Association of America
5721:
5447:
5417:
5353:
5328:
5099:
4962:counterpart of the turn, equivalent to
3152:
3115:
3062:
3025:
2979:
2948:
2911:
2875:
2865:
2837:
2827:
2790:
2718:
2649:
2575:
2498:
2352:
2251:
2140:
1987:
1844:
1789:
1671:
1630:
1566:
1529:
1443:
1406:
618:of 0.36°, which can also be written as
7568:
7347:
7207:
6934:
6842:
6634:
6572:
6549:The Tau Manifesto - With Michael Hartl
6469:
6330:
6222:
5832:
5448:Lapilli, Claudio Daniel (2018-10-25).
5418:Lapilli, Claudio Daniel (2016-05-11).
864:Essay Explaining the Properties of Air
7022:
6773:
6705:. Toronto, Ontario, Canada: 627–629.
6521:
6423:
6372:
6314:Lettres inédites d'Euler à d'Alembert
6310:
6245:
6199:
5922:
5916:
5790:/ Howard A. Doyle Publishing Company.
5779:
5665:
5633:Macdonald & Co. (Publishers) Ltd.
5619:
5567:
5518:
5271:. 978-3-528-08441-7, 978-3-32283606-9
5146:
4412:(Space and time), and adopted in the
2441:is the boundary of a disk containing
874:for the 3.14... constant in his 1736
866:, where it was denoted by the letter
495:
7475:
7213:
7170:
7105:
6805:
6660:
6424:Euler, Leonhard (1707–1783) (1922).
5477:
510:'full angle') for turns. Covered in
421:), equal to the ratio of a circle's
25:
7076:
6470:Segner, Johann Andreas von (1761).
5072:Newtonian Dynamics: An Introduction
4492:Physical quantity § Components
1083: turn would be represented as
893:Introductio in analysin infinitorum
883:Introductio in analysin infinitorum
870:. Euler would later use the letter
292:, one turn also corresponds to one
111:tr, pla, rev, cyc
13:
7254:"package math - pkg.odin-lang.org"
6848:"On Pi Day, is 'pi' under attack?"
6490:
6143:
5668:"Chapter 8: Keeping Track of Time"
4540:
4530:
4324:International System of Quantities
3178:
1880:-sphere volume recurrence relation
1057:to represent the circle constant:
708:Pi § Adoption of the symbol π
480:
383:
14:
7602:
7552:
7450:The International System of Units
7176:
6476:(in Latin). Renger. p. 374.
6333:The American Mathematical Monthly
6202:"William Jones: The First Use of
5478:Paul, Matthias R. (2016-01-12) .
5021:Original version, current version
3068:
3034:
1259:In 2012, the educational website
1053:proposed to use the Greek letter
42:Draft:Tau (mathematical constant)
7386:from the original on 2013-09-28.
6703:Proceedings of the 2014 IEEE GEM
6398:English translation by Ian Bruce
6394:rationem diametri ad peripheriam
6288:English translation by Ian Bruce
6212:. McGraw–Hill. pp. 346–347.
4613:rev, r, cyc, c
4400:where 𝜑 denotes the measure of
4260:
1341:. For a more complete list, see
1143:
1129:is the number of radians in one
895:, Euler instead used the letter
689:equal parts for other values of
397:proposed using the Greek letter
30:
7330:from the original on 2019-07-22
7316:Harremoës, Peter (2018-11-17).
7123:from the original on 2023-07-18
7094:from the original on 2019-07-22
7065:from the original on 2019-07-22
7036:from the original on 2019-07-22
7011:from the original on 2019-07-29
7001:"math — Mathematical functions"
6982:from the original on 2019-07-22
6952:from the original on 2023-03-26
6923:from the original on 2023-07-18
6894:from the original on 2019-06-18
6862:from the original on 2018-12-19
6788:from the original on 2019-07-18
6628:
6617:from the original on 2019-07-18
6539:
6463:
6438:from the original on 2017-10-16
6417:
6366:
6304:
6272:from the original on 2016-04-01
6239:
5844:from the original on 2019-06-30
5767:Volksbildungshaus Wiener Urania
5666:Klein, Herbert Arthur (2012) .
5623:(1962). Chandler, M. H. (ed.).
5594:from the original on 2023-07-18
5545:from the original on 2023-07-18
5490:from the original on 2019-08-05
5460:from the original on 2019-08-06
5430:from the original on 2017-08-10
5420:"RE: newRPL: Handling of units"
5400:from the original on 2019-05-10
5367:from the original on 2019-08-06
5342:from the original on 2019-06-22
5289:Kurzweil, Peter (2013-03-09) .
5210:McMillan, Robert (2020-03-13).
5155:from the original on 2019-06-28
5125:from the original on 2023-07-18
5042:
5033:
5024:
5015:
1226:, contains a natural factor of
990:. Crease used the Greek letter
599:
596:) as mode and unit since 2019.
487:
7348:Abbott, Stephen (April 2012).
7113:"std::f64::consts::TAU - Rust"
6583:The Mathematical Intelligencer
5929:Synopsis Palmariorum Matheseos
5780:Hayes, Eugene Nelson (1975) .
5738:10.1080/01621459.1922.10502455
5147:Hartl, Michael (2019-03-14) .
5006:
2563:
2557:
2486:
2480:
2386:
2380:
2339:
2333:
2288:
2282:
2238:
2232:
2171:
2165:
2133:
2127:
2097:
2091:
2059:
2053:
2021:
2015:
1980:
1974:
1944:
1938:
1906:
1900:
538:
521:(October 2010), the so-called
267:at its center. It is equal to
1:
6830:10.1016/S0262-4079(11)60036-5
6774:Hartl, Michael (2010-03-14).
6635:Crease, Robert (2008-02-01).
5873:Barnes & Noble Publishing
5751:Schiffner, Friedrich (1965).
5069:Fitzpatrick, Richard (2021).
5055:
4414:International System of Units
3755:
3749:
922:
340:), rotating objects, and the
7369:10.4169/mathhorizons.19.4.34
7240:.NET Reference Documentation
6970:Coghlan, Nick (2017-02-25).
6210:A Source Book in Mathematics
6200:Smith, David Eugene (1929).
6131:
6066:
6001:
5932:. London: J. Wale. pp.
5886:Schwartzman, Steven (1994).
5571:WP 43S Reference Manual
5185:. 2011-06-30. Archived from
3249:Conversion of common angles
2467:Standard normal distribution
809:(pi over rho) to denote the
382:radians, some have proposed
21:360 degrees (disambiguation)
7:
4919:
1344:List of formulae involving
1016:{\displaystyle \psi =2\pi }
543:The scientific calculators
535:in the EU and Switzerland.
478:
39:It has been suggested that
10:
7607:
7005:Python 3.7.0 documentation
5684:Simon & Schuster, Inc.
5635:/ Rathbone Books Limited.
5631:(1 ed.). London, UK:
5522:WP 43S Owner's Manual
5253:(in German) (1 ed.).
1513:Circumference of a circle
1323:-promoter Peter Harremoës.
1278:Desmos graphing calculator
763:The meaning of the symbol
705:
645:Binary fractions of a turn
603:
18:
7350:"My Conversion to Tauism"
6972:"PEP 628 -- Add math.tau"
5394:Schweizerischer Bundesrat
5363:(in German). 2009-03-11.
5338:(in German). 1980-02-15.
5305:10.1007/978-3-322-92920-4
4639:
4635:
4617:
4609:
4599:
4594:
4421:quantity of dimension one
4308:
4296:
4284:
4274:
4269:
3745:
3278:
3258:
2219:Cauchy's integral formula
575:in 2017. An angular mode
533:legal unit of measurement
527:('full angle') is not an
222:
206:
171:
137:
133:
115:
107:
97:
92:
74:
69:
56:Proposed since July 2024.
7295:10.14736/kyb-2016-6-0943
6502:Encyclopaedia Brittanica
6373:Euler, Leonhard (1736).
6246:Euler, Leonhard (1727).
6186:; and by means thereof,
5676:Dover Publications, Inc.
5392:(in Swiss High German).
4999:
4681:In programming languages
2627:Stirling's approximation
641:carry milliturn scales.
256:measurement that is the
7318:"Al-Kashi's constant τ"
6747:10.1145/3325424.3330210
6573:Palais, Robert (2001).
6375:"Ch. 3 Prop. 34 Cor. 1"
6329:English translation in
5568:Bonin, Walter (2019) .
5519:Bonin, Walter (2019) .
5396:. 1994-11-23. 941.202.
4665:dimensional homogeneity
4402:rotational displacement
3090:reduced Planck constant
2434:{\displaystyle \gamma }
1756:with unit circumradius
813:of a circle (i.e., the
6643:. Institute of Physics
6159:
4946:Revolutions per minute
4586:revolutions per minute
4554:
4476:
4406:
4391:
3207:
3165:
3131:
3075:
3041:
2995:
2891:
2758:
2692:
2614:
2540:
2461:in the complex plane.
2455:
2435:
2414:
2316:
2178:
2104:
2028:
1951:
1858:
1806:
1701:
1650:
1579:
1545:
1465:
1428:
1017:
973:
931:Peter Harremoës (2010)
777:
742:
734:
726:
579:was suggested for the
523:
506:
461:dimensionless quantity
446:
411:
376:
329:revolutions per minute
7581:Mathematical concepts
7201:Java 19 documentation
6942:"Supported Functions"
6225:"Pi through the ages"
6223:Veling, Anne (2001).
6206:for the Circle Ratio"
6160:
5783:Trackers of the Skies
5480:"RE: WP-32S in 2016?"
4888:std::f64::consts::TAU
4555:
4477:
4392:
4346:
4342:number of revolutions
3210:One turn is equal to
3186:
3166:
3132:
3076:
3042:
2996:
2892:
2759:
2693:
2615:
2541:
2456:
2436:
2415:
2317:
2179:
2105:
2029:
1952:
1859:
1807:
1702:
1651:
1580:
1546:
1466:
1429:
1104: rad instead of
1018:
974:
778:
740:
732:
715:
559:in 2016, and for the
447:
445:{\displaystyle 2\pi }
412:
410:{\displaystyle \tau }
377:
375:{\displaystyle 2\pi }
334:electromagnetic coils
7576:Units of plane angle
6917:blog.khanacademy.org
6590:(3). New York, USA:
6403:10 June 2016 at the
6293:10 June 2016 at the
5967:
4567:(s). Common related
4517:
4500:rotational frequency
4434:
4358:
3142:
3105:
3052:
3015:
2902:
2781:
2703:
2634:
2551:
2474:
2445:
2425:
2327:
2226:
2114:
2040:
1961:
1887:
1817:
1762:
1661:
1620:
1556:
1519:
1439:
1402:
998:
946:
934:Michael Hartl (2010)
776:{\displaystyle \pi }
767:
655:, also known as the
500:The German standard
433:
401:
391:with a single letter
363:
359:Because one turn is
49:into this article. (
6887:Scientific American
6822:2011NewSc.209...23A
6776:"The Tau Manifesto"
5680:Courier Corporation
5390:Einheitenverordnung
5317:. 978-3-322-92921-1
5219:Wall Street Journal
5149:"The Tau Manifesto"
4994:Twist (mathematics)
4956:Spat (angular unit)
4630:... is equal to ...
3250:
1380:Angle subtended by
1354:
1337:is used instead of
1173:is used instead of
1159:visually resembles
1030:, Θ, to represent 2
921:Joseph Lindenburg (
531:. However, it is a
128:... is equal to ...
93:General information
7507:"ISO 80000-3:2006"
7258:Odin documentation
7164:Unreal Engine Docs
6637:"Constant failure"
6600:10.1007/bf03026846
6155:
6128:
6106:
6084:
6063:
6041:
6019:
5998:
5983:
5840:. blogs.msdn.com.
5454:newRPL User Manual
5134:(1+iii+32+1 pages)
4756:math_constants.Tau
4661:dimensionless unit
4649:
4641:
4569:units of frequency
4550:
4472:
4387:
3248:
3208:
3161:
3156:
3127:
3122:
3071:
3066:
3037:
3032:
2991:
2983:
2952:
2915:
2887:
2879:
2869:
2841:
2831:
2797:
2754:
2722:
2688:
2656:
2610:
2579:
2536:
2505:
2451:
2431:
2410:
2356:
2312:
2258:
2174:
2144:
2100:
2024:
1994:
1947:
1854:
1848:
1802:
1796:
1749:Area of a regular
1697:
1685:
1646:
1634:
1575:
1570:
1541:
1536:
1461:
1454:
1424:
1417:
1353:
1013:
988:John Horton Conway
969:
928:John Fisher (2004)
773:
743:
735:
727:
639:satellite watching
606:Angle § Units
496:EU and Switzerland
442:
407:
372:
318:units of frequency
316:). Common related
232:
224:
216:
208:
181:
173:
147:
139:
7560:The Tau Manifesto
7480:(2008 ed.).
7463:978-92-822-2272-0
7117:doc.rust-lang.org
6844:Landau, Elizabeth
6134:
6127:
6105:
6083:
6069:
6062:
6040:
6018:
6004:
5997:
5982:
5834:Hargreaves, Shawn
5765:. Wien, Austria:
5753:Wähnl, Maria Emma
5086:978-1-000-50953-3
4941:Angle of rotation
4917:
4916:
4763:Not yet released
4669:kinds of quantity
4657:
4656:
4618:Conversions
4580:cycles per second
4565:reciprocal second
4548:
4469:
4451:
4450:
4385:
4382:
4338:physical quantity
4320:
4319:
4255:
4254:
3176:
3175:
3098:Angular frequency
2989:
2958:
2928:
2885:
2847:
2810:
2774:th roots of unity
2742:
2727:
2676:
2661:
2606:
2581:
2580:
2532:
2507:
2506:
2454:{\displaystyle a}
2401:
2362:
2303:
2264:
2073:
1920:
1852:
1834:
1800:
1779:
1680:
1587:The length of an
1459:
1452:
1422:
1415:
483:for the formula.)
469:, defined as the
323:cycles per second
238:
237:
116:Conversions
82:Counterclockwise
63:
62:
58:
7598:
7546:
7545:
7543:
7542:
7528:
7522:
7521:
7519:
7518:
7503:
7494:
7491:
7489:
7488:
7473:
7467:
7466:
7455:
7445:
7439:
7435:
7433:
7432:
7417:
7406:
7405:
7394:
7388:
7387:
7385:
7354:
7345:
7339:
7338:
7336:
7335:
7329:
7322:
7313:
7307:
7306:
7288:
7268:
7262:
7261:
7250:
7244:
7243:
7236:"Math.Tau Field"
7232:
7226:
7225:
7211:
7205:
7204:
7193:
7187:
7186:
7183:bugs.openjdk.org
7174:
7168:
7167:
7156:
7150:
7149:
7138:
7132:
7131:
7129:
7128:
7109:
7103:
7102:
7100:
7099:
7080:
7074:
7073:
7071:
7070:
7051:
7045:
7044:
7042:
7041:
7026:
7020:
7019:
7017:
7016:
6997:
6991:
6990:
6988:
6987:
6967:
6961:
6960:
6958:
6957:
6938:
6932:
6931:
6929:
6928:
6913:"Happy Tau Day!"
6909:
6903:
6902:
6900:
6899:
6877:
6871:
6870:
6868:
6867:
6840:
6834:
6833:
6803:
6797:
6796:
6794:
6793:
6787:
6780:
6771:
6765:
6764:
6762:
6761:
6741:(Keynote): 1–2.
6727:
6721:
6720:
6718:
6717:
6691:
6685:
6683:
6681:
6680:
6674:
6668:. Archived from
6667:
6658:
6652:
6651:
6649:
6648:
6632:
6626:
6625:
6623:
6622:
6616:
6579:
6570:
6561:
6560:
6558:
6557:
6543:
6537:
6536:
6519:
6513:
6512:
6510:
6509:
6494:
6488:
6487:
6485:
6481:
6467:
6461:
6460:
6454:
6446:
6444:
6443:
6421:
6415:
6413:
6396:
6393:
6370:
6364:
6363:
6360:
6328:
6326:
6308:
6302:
6300:
6286:
6284:
6278:
6277:
6271:
6252:
6243:
6237:
6236:
6231:. Archived from
6220:
6214:
6213:
6205:
6197:
6194:
6175:
6164:
6162:
6161:
6156:
6135:
6130:
6129:
6126:
6125:
6113:
6107:
6104:
6103:
6091:
6087:
6085:
6076:
6070:
6065:
6064:
6061:
6060:
6048:
6042:
6039:
6038:
6026:
6022:
6020:
6011:
6005:
6000:
5999:
5990:
5984:
5975:
5971:
5920:
5914:
5913:
5909:978-0-88385511-9
5893:
5883:
5877:
5876:
5859:
5853:
5852:
5850:
5849:
5830:
5824:
5823:
5821:
5820:
5798:
5792:
5791:
5777:
5771:
5770:
5748:
5742:
5741:
5732:(137): 108–109.
5719:
5713:
5711:
5709:
5708:
5693:978-0-48614497-9
5686:). p. 102.
5663:
5654:
5652:
5630:
5617:
5608:
5602:
5600:
5599:
5593:
5584:978-1-72950106-1
5576:
5565:
5559:
5553:
5551:
5550:
5544:
5535:978-1-72950098-9
5527:
5516:
5510:
5509:
5496:
5495:
5475:
5469:
5468:
5466:
5465:
5445:
5439:
5438:
5436:
5435:
5415:
5409:
5408:
5406:
5405:
5382:
5376:
5375:
5373:
5372:
5357:
5351:
5350:
5348:
5347:
5332:
5326:
5325:
5323:
5322:
5314:978-3-32292920-4
5286:
5280:
5279:
5277:
5276:
5268:978-3-32283606-9
5244:
5238:
5237:
5235:
5234:
5215:
5207:
5198:
5197:
5195:
5194:
5173:
5164:
5163:
5161:
5160:
5144:
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5133:
5131:
5130:
5124:
5113:
5103:
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5096:
5094:
5093:
5066:
5049:
5046:
5040:
5037:
5031:
5028:
5022:
5019:
5013:
5010:
4989:Modulo operation
4968:
4951:Repeating circle
4935:Cycle per second
4720:System.MathF.Tau
4689:
4688:
4686:the same value.
4650:
4642:
4592:
4591:
4559:
4557:
4556:
4551:
4549:
4547:
4543:
4537:
4533:
4527:
4509:
4481:
4479:
4478:
4473:
4471:
4470:
4467:
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4448:
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4396:
4394:
4393:
4388:
4386:
4384:
4383:
4380:
4368:
4267:
4266:
4244:
4223:
4221:
4220:
4217:
4214:
4213:
4202:
4200:
4199:
4196:
4193:
4184:
4182:
4181:
4178:
4175:
4158:
4152:
4150:
4149:
4146:
4143:
4134:
4132:
4131:
4128:
4125:
4108:
4106:
4105:
4102:
4099:
4098:
4087:
4085:
4084:
4081:
4078:
4069:
4067:
4066:
4063:
4060:
4050:
4048:
4047:
4044:
4041:
4037:
4026:
4024:
4023:
4020:
4017:
4016:
4005:
4003:
4002:
3999:
3996:
3987:
3985:
3984:
3981:
3978:
3961:
3959:
3958:
3955:
3952:
3951:
3941:
3939:
3938:
3935:
3932:
3923:
3921:
3920:
3917:
3914:
3897:
3895:
3894:
3891:
3888:
3887:
3876:
3874:
3873:
3870:
3867:
3858:
3856:
3855:
3852:
3849:
3839:
3837:
3836:
3833:
3830:
3826:
3815:
3813:
3812:
3809:
3806:
3805:
3795:
3793:
3792:
3789:
3786:
3777:
3775:
3774:
3771:
3768:
3757:
3751:
3742:
3740:
3739:
3738:
3733:
3730:
3713:
3711:
3710:
3707:
3704:
3703:
3693:
3691:
3690:
3687:
3684:
3675:
3673:
3672:
3669:
3666:
3649:
3647:
3646:
3643:
3640:
3639:
3629:
3627:
3626:
3623:
3620:
3611:
3609:
3608:
3605:
3602:
3592:
3590:
3589:
3586:
3583:
3579:
3568:
3566:
3565:
3562:
3559:
3558:
3548:
3546:
3545:
3542:
3539:
3530:
3528:
3527:
3524:
3521:
3504:
3502:
3501:
3498:
3495:
3494:
3484:
3482:
3481:
3478:
3475:
3466:
3464:
3463:
3460:
3457:
3447:
3445:
3444:
3441:
3438:
3434:
3423:
3421:
3420:
3417:
3414:
3413:
3403:
3401:
3400:
3397:
3394:
3385:
3383:
3382:
3379:
3376:
3366:
3364:
3363:
3360:
3357:
3353:
3342:
3340:
3339:
3336:
3333:
3332:
3322:
3320:
3319:
3316:
3313:
3304:
3302:
3301:
3298:
3295:
3251:
3247:
3232:
3231:
3228:
3225:
3222:
3216:
3205:
3170:
3168:
3167:
3162:
3157:
3136:
3134:
3133:
3128:
3123:
3087:
3080:
3078:
3077:
3072:
3067:
3046:
3044:
3043:
3038:
3033:
3000:
2998:
2997:
2992:
2990:
2985:
2984:
2973:
2959:
2954:
2953:
2942:
2931:
2930:
2929:
2921:
2916:
2896:
2894:
2893:
2888:
2886:
2881:
2880:
2870:
2862:
2848:
2843:
2842:
2832:
2824:
2813:
2812:
2811:
2803:
2798:
2773:
2763:
2761:
2760:
2755:
2753:
2752:
2747:
2743:
2735:
2728:
2723:
2716:
2697:
2695:
2694:
2689:
2687:
2686:
2681:
2677:
2669:
2662:
2657:
2647:
2619:
2617:
2616:
2611:
2609:
2608:
2607:
2602:
2601:
2592:
2582:
2574:
2570:
2545:
2543:
2542:
2537:
2535:
2534:
2533:
2528:
2527:
2518:
2508:
2497:
2493:
2460:
2458:
2457:
2452:
2440:
2438:
2437:
2432:
2419:
2417:
2416:
2411:
2402:
2400:
2389:
2375:
2373:
2372:
2363:
2361:
2357:
2346:
2321:
2319:
2318:
2313:
2304:
2302:
2291:
2277:
2275:
2274:
2265:
2263:
2259:
2245:
2213:
2199:
2183:
2181:
2180:
2175:
2164:
2163:
2145:
2126:
2125:
2109:
2107:
2106:
2101:
2090:
2089:
2074:
2066:
2052:
2051:
2033:
2031:
2030:
2025:
2014:
2013:
1995:
1973:
1972:
1956:
1954:
1953:
1948:
1937:
1936:
1921:
1913:
1899:
1898:
1879:
1873:
1863:
1861:
1860:
1855:
1853:
1843:
1835:
1827:
1811:
1809:
1808:
1803:
1801:
1788:
1780:
1772:
1753:
1743:
1739:
1737:
1736:
1733:
1730:
1718:
1706:
1704:
1703:
1698:
1696:
1695:
1686:
1681:
1673:
1655:
1653:
1652:
1647:
1645:
1644:
1635:
1613:Area of a circle
1606:
1596:
1584:
1582:
1581:
1576:
1571:
1550:
1548:
1547:
1542:
1537:
1508:
1506:
1504:
1503:
1500:
1497:
1490:
1488:
1487:
1484:
1481:
1470:
1468:
1467:
1462:
1460:
1457:
1455:
1453:
1445:
1433:
1431:
1430:
1425:
1423:
1420:
1418:
1416:
1408:
1395:
1393:
1392:
1389:
1386:
1372:
1364:
1355:
1352:
1347:
1340:
1336:
1322:
1275:
1268:
1254:
1241:
1239:
1238:
1235:
1232:
1225:
1220:
1218:
1217:
1214:
1211:
1199:
1195:
1188:
1181:Euler's identity
1178:
1172:
1162:
1158:
1154:
1153:
1150:
1149:
1136:
1128:
1124:
1123:
1121:
1120:
1117:
1114:
1103:
1102:
1100:
1099:
1096:
1093:
1082:
1080:
1079:
1076:
1073:
1066:
1045:
1041:
1033:
1022:
1020:
1019:
1014:
984:Robert P. Crease
978:
976:
975:
970:
941:
924:
916:
915:
906:
902:
898:
873:
869:
846:
842:
841:
839:
838:
833:
830:
819:William Oughtred
808:
807:
805:
804:
799:
796:
782:
780:
779:
774:
751:
750:
724:
692:
688:
680:
678:
677:
674:
671:
613:
593:
586:
526:
520:
509:
484:
451:
449:
448:
443:
416:
414:
413:
408:
390:
381:
379:
378:
373:
352:, respectively;
275:
233:
225:
217:
209:
202:
200:
196:
188:
182:
174:
167:
165:
162:
154:
148:
140:
79:
67:
66:
54:
34:
33:
26:
7606:
7605:
7601:
7600:
7599:
7597:
7596:
7595:
7566:
7565:
7555:
7550:
7549:
7540:
7538:
7530:
7529:
7525:
7516:
7514:
7505:
7504:
7497:
7486:
7484:
7474:
7470:
7464:
7453:
7447:
7446:
7442:
7430:
7428:
7419:
7418:
7409:
7397:
7395:
7391:
7383:
7352:
7346:
7342:
7333:
7331:
7327:
7320:
7314:
7310:
7269:
7265:
7252:
7251:
7247:
7234:
7233:
7229:
7212:
7208:
7195:
7194:
7190:
7175:
7171:
7158:
7157:
7153:
7140:
7139:
7135:
7126:
7124:
7111:
7110:
7106:
7097:
7095:
7082:
7081:
7077:
7068:
7066:
7053:
7052:
7048:
7039:
7037:
7028:
7027:
7023:
7014:
7012:
6999:
6998:
6994:
6985:
6983:
6968:
6964:
6955:
6953:
6946:help.desmos.com
6940:
6939:
6935:
6926:
6924:
6911:
6910:
6906:
6897:
6895:
6878:
6874:
6865:
6863:
6841:
6837:
6804:
6800:
6791:
6789:
6785:
6778:
6772:
6768:
6759:
6757:
6728:
6724:
6715:
6713:
6692:
6688:
6678:
6676:
6672:
6665:
6659:
6655:
6646:
6644:
6633:
6629:
6620:
6618:
6614:
6592:Springer-Verlag
6577:
6571:
6564:
6555:
6553:
6545:
6544:
6540:
6523:Euler, Leonhard
6520:
6516:
6507:
6505:
6496:
6495:
6491:
6483:
6479:
6468:
6464:
6448:
6447:
6441:
6439:
6422:
6418:
6408:
6405:Wayback Machine
6388:
6371:
6367:
6358:
6345:10.2307/2973441
6324:
6309:
6305:
6298:
6295:Wayback Machine
6282:
6275:
6273:
6269:
6250:
6244:
6240:
6221:
6217:
6203:
6192:
6166:
6165:
6121:
6117:
6111:
6099:
6095:
6089:
6088:
6086:
6074:
6056:
6052:
6046:
6034:
6030:
6024:
6023:
6021:
6009:
5988:
5973:
5972:
5970:
5968:
5965:
5964:
5963:
5940:. p. 263:
5921:
5917:
5910:
5884:
5880:
5868:A History of Pi
5860:
5856:
5847:
5845:
5831:
5827:
5818:
5816:
5800:
5799:
5795:
5778:
5774:
5749:
5745:
5720:
5716:
5706:
5704:
5694:
5682:(originally by
5664:
5657:
5618:
5611:
5597:
5595:
5591:
5585:
5574:
5566:
5562:
5548:
5546:
5542:
5536:
5525:
5517:
5513:
5493:
5491:
5476:
5472:
5463:
5461:
5446:
5442:
5433:
5431:
5416:
5412:
5403:
5401:
5384:
5383:
5379:
5370:
5368:
5359:
5358:
5354:
5345:
5343:
5334:
5333:
5329:
5320:
5318:
5315:
5299:. p. 403.
5297:Springer-Verlag
5287:
5283:
5274:
5272:
5269:
5261:. p. 421.
5259:Springer-Verlag
5245:
5241:
5232:
5230:
5208:
5201:
5192:
5190:
5182:Telegraph India
5175:
5174:
5167:
5158:
5156:
5145:
5138:
5128:
5126:
5122:
5111:
5105:
5104:
5100:
5091:
5089:
5087:
5079:. p. 116.
5067:
5063:
5058:
5053:
5052:
5047:
5043:
5038:
5034:
5029:
5025:
5020:
5016:
5011:
5007:
5002:
4963:
4922:
4716:System.Math.Tau
4683:
4648:
4640:
4539:
4538:
4529:
4528:
4526:
4518:
4515:
4514:
4507:
4488:
4466:
4462:
4443:
4435:
4432:
4431:
4379:
4372:
4367:
4359:
4356:
4355:
4287:
4277:
4263:
4257:
4242:
4218:
4215:
4211:
4209:
4208:
4206:
4197:
4194:
4191:
4190:
4188:
4179:
4176:
4173:
4172:
4170:
4156:
4147:
4144:
4141:
4140:
4138:
4129:
4126:
4123:
4122:
4120:
4103:
4100:
4096:
4094:
4093:
4091:
4082:
4079:
4076:
4075:
4073:
4064:
4061:
4058:
4057:
4055:
4045:
4042:
4039:
4038:
4035:
4033:
4021:
4018:
4014:
4012:
4011:
4009:
4000:
3997:
3994:
3993:
3991:
3982:
3979:
3976:
3975:
3973:
3956:
3953:
3949:
3948:
3947:
3945:
3936:
3933:
3930:
3929:
3927:
3918:
3915:
3912:
3911:
3909:
3892:
3889:
3885:
3883:
3882:
3880:
3871:
3868:
3865:
3864:
3862:
3853:
3850:
3847:
3846:
3844:
3834:
3831:
3828:
3827:
3824:
3822:
3810:
3807:
3803:
3802:
3801:
3799:
3790:
3787:
3784:
3783:
3781:
3772:
3769:
3766:
3765:
3763:
3736:
3734:
3731:
3728:
3727:
3725:
3708:
3705:
3701:
3700:
3699:
3697:
3688:
3685:
3682:
3681:
3679:
3670:
3667:
3664:
3663:
3661:
3644:
3641:
3637:
3636:
3635:
3633:
3624:
3621:
3618:
3617:
3615:
3606:
3603:
3600:
3599:
3597:
3587:
3584:
3581:
3580:
3577:
3575:
3563:
3560:
3556:
3555:
3554:
3552:
3543:
3540:
3537:
3536:
3534:
3525:
3522:
3519:
3518:
3516:
3499:
3496:
3492:
3491:
3490:
3488:
3479:
3476:
3473:
3472:
3470:
3461:
3458:
3455:
3454:
3452:
3442:
3439:
3436:
3435:
3432:
3430:
3418:
3415:
3411:
3410:
3409:
3407:
3398:
3395:
3392:
3391:
3389:
3380:
3377:
3374:
3373:
3371:
3361:
3358:
3355:
3354:
3351:
3349:
3337:
3334:
3330:
3329:
3328:
3326:
3317:
3314:
3311:
3310:
3308:
3299:
3296:
3293:
3292:
3290:
3229:
3226:
3223:
3220:
3218:
3211:
3200:
3181:
3179:Unit conversion
3151:
3143:
3140:
3139:
3114:
3106:
3103:
3102:
3083:
3061:
3053:
3050:
3049:
3024:
3016:
3013:
3012:
3008:Planck constant
2978:
2974:
2972:
2947:
2943:
2941:
2920:
2910:
2909:
2905:
2903:
2900:
2899:
2874:
2864:
2863:
2861:
2836:
2826:
2825:
2823:
2802:
2789:
2788:
2784:
2782:
2779:
2778:
2771:
2748:
2734:
2730:
2729:
2717:
2715:
2704:
2701:
2700:
2682:
2668:
2664:
2663:
2648:
2646:
2635:
2632:
2631:
2597:
2593:
2591:
2587:
2583:
2569:
2552:
2549:
2548:
2523:
2519:
2517:
2513:
2509:
2492:
2475:
2472:
2471:
2446:
2443:
2442:
2426:
2423:
2422:
2390:
2376:
2374:
2368:
2364:
2351:
2350:
2345:
2328:
2325:
2324:
2292:
2278:
2276:
2270:
2266:
2250:
2249:
2244:
2227:
2224:
2223:
2207:
2201:
2200:
2193:
2187:
2153:
2149:
2139:
2121:
2117:
2115:
2112:
2111:
2079:
2075:
2065:
2047:
2043:
2041:
2038:
2037:
2003:
1999:
1986:
1968:
1964:
1962:
1959:
1958:
1926:
1922:
1912:
1894:
1890:
1888:
1885:
1884:
1875:
1871:
1842:
1826:
1818:
1815:
1814:
1787:
1771:
1763:
1760:
1759:
1751:
1734:
1731:
1728:
1727:
1725:
1720:
1714:
1691:
1687:
1672:
1670:
1662:
1659:
1658:
1640:
1636:
1629:
1621:
1618:
1617:
1598:
1592:
1565:
1557:
1554:
1553:
1528:
1520:
1517:
1516:
1501:
1498:
1495:
1494:
1492:
1485:
1482:
1477:
1476:
1474:
1473:
1456:
1444:
1442:
1440:
1437:
1436:
1419:
1407:
1405:
1403:
1400:
1399:
1390:
1387:
1384:
1383:
1381:
1368:
1362:
1345:
1338:
1328:
1320:
1273:
1264:
1250:
1236:
1233:
1230:
1229:
1227:
1215:
1212:
1209:
1208:
1206:
1201:
1197:
1190:
1183:
1174:
1168:
1160:
1156:
1155:sound. Second,
1146:
1142:
1134:
1126:
1118:
1115:
1109:
1108:
1106:
1105:
1097:
1094:
1088:
1087:
1085:
1084:
1077:
1074:
1071:
1070:
1068:
1058:
1043:
1039:
1031:
999:
996:
995:
947:
944:
943:
939:
913:
911:
904:
900:
896:
871:
867:
844:
834:
831:
826:
825:
823:
822:
800:
797:
792:
791:
789:
788:
768:
765:
764:
748:
746:
722:
710:
702:
690:
686:
675:
672:
669:
668:
666:
611:
608:
602:
591:
584:
578:
541:
514:
498:
490:
434:
431:
430:
402:
399:
398:
385:
364:
361:
360:
354:metric prefixes
268:
258:angular measure
252:) is a unit of
231:
223:
215:
207:
198:
194:
192:
190:
183:
180:
172:
163:
160:
158:
156:
149:
146:
138:
88:
87:
59:
35:
31:
24:
17:
12:
11:
5:
7604:
7594:
7593:
7588:
7583:
7578:
7564:
7563:
7554:
7553:External links
7551:
7548:
7547:
7523:
7495:
7468:
7462:
7440:
7423:(2 ed.).
7407:
7389:
7340:
7308:
7279:(6): 943–966.
7263:
7245:
7227:
7206:
7188:
7169:
7151:
7133:
7104:
7075:
7046:
7030:"Perl 6 terms"
7021:
6992:
6962:
6933:
6919:. 2012-06-28.
6904:
6872:
6846:(2011-03-14).
6835:
6798:
6766:
6722:
6686:
6653:
6627:
6562:
6538:
6514:
6489:
6462:
6416:
6365:
6303:
6238:
6235:on 2009-07-02.
6215:
6167:3.14159, &
6154:
6151:
6148:
6145:
6141:
6138:
6133:
6124:
6120:
6116:
6110:
6102:
6098:
6094:
6082:
6079:
6073:
6068:
6059:
6055:
6051:
6045:
6037:
6033:
6029:
6017:
6014:
6008:
6003:
5996:
5993:
5987:
5981:
5978:
5950:of particular
5924:Jones, William
5915:
5908:
5878:
5863:Beckmann, Petr
5854:
5825:
5793:
5788:Academic Press
5772:
5743:
5728:. Short Note.
5714:
5692:
5655:
5609:
5583:
5560:
5534:
5511:
5470:
5440:
5410:
5377:
5352:
5327:
5313:
5281:
5267:
5239:
5199:
5165:
5136:
5114:. London, UK:
5098:
5085:
5060:
5059:
5057:
5054:
5051:
5050:
5041:
5032:
5023:
5014:
5004:
5003:
5001:
4998:
4997:
4996:
4991:
4986:
4979:
4974:
4953:
4948:
4943:
4938:
4928:
4921:
4918:
4915:
4914:
4911:
4908:
4903:
4897:
4896:
4893:
4890:
4885:
4879:
4878:
4876:
4874:
4865:
4859:
4858:
4855:
4852:
4847:
4841:
4840:
4837:
4834:
4825:
4819:
4818:
4815:
4812:
4807:
4801:
4800:
4797:
4794:
4789:
4783:
4782:
4779:
4776:
4771:
4765:
4764:
4761:
4758:
4753:
4747:
4746:
4743:
4740:
4735:
4729:
4728:
4725:
4722:
4713:
4703:
4702:
4701:Year Released
4699:
4696:
4693:
4682:
4679:
4655:
4654:
4646:
4637:
4636:
4633:
4632:
4627:
4620:
4619:
4615:
4614:
4611:
4607:
4606:
4601:
4597:
4596:
4561:
4560:
4546:
4542:
4536:
4532:
4525:
4522:
4504:rate of change
4486:
4483:
4482:
4465:
4461:
4458:
4455:
4447:
4442:
4439:
4398:
4397:
4378:
4375:
4371:
4366:
4363:
4318:
4317:
4312:
4306:
4305:
4300:
4294:
4293:
4288:
4286:Common symbols
4285:
4282:
4281:
4278:
4275:
4272:
4271:
4262:
4259:
4253:
4252:
4249:
4246:
4239:
4236:
4232:
4231:
4228:
4225:
4204:
4186:
4167:
4166:
4163:
4160:
4154:
4136:
4117:
4116:
4113:
4110:
4089:
4071:
4052:
4051:
4031:
4028:
4007:
3989:
3970:
3969:
3966:
3963:
3943:
3925:
3906:
3905:
3902:
3899:
3878:
3860:
3841:
3840:
3820:
3817:
3797:
3779:
3760:
3759:
3753:
3747:
3744:
3722:
3721:
3718:
3715:
3695:
3677:
3658:
3657:
3654:
3651:
3631:
3613:
3594:
3593:
3573:
3570:
3550:
3532:
3513:
3512:
3509:
3506:
3486:
3468:
3449:
3448:
3428:
3425:
3405:
3387:
3368:
3367:
3347:
3344:
3324:
3306:
3287:
3286:
3283:
3280:
3277:
3273:
3272:
3267:
3262:
3257:
3180:
3177:
3174:
3173:
3171:
3160:
3155:
3150:
3147:
3137:
3126:
3121:
3118:
3113:
3110:
3100:
3094:
3093:
3081:
3070:
3065:
3060:
3057:
3047:
3036:
3031:
3028:
3023:
3020:
3010:
3004:
3003:
3001:
2988:
2982:
2977:
2971:
2968:
2965:
2962:
2957:
2951:
2946:
2940:
2937:
2934:
2927:
2924:
2919:
2914:
2908:
2897:
2884:
2878:
2873:
2868:
2860:
2857:
2854:
2851:
2846:
2840:
2835:
2830:
2822:
2819:
2816:
2809:
2806:
2801:
2796:
2793:
2787:
2776:
2767:
2766:
2764:
2751:
2746:
2741:
2738:
2733:
2726:
2721:
2714:
2711:
2708:
2698:
2685:
2680:
2675:
2672:
2667:
2660:
2655:
2652:
2645:
2642:
2639:
2629:
2623:
2622:
2620:
2605:
2600:
2596:
2590:
2586:
2578:
2573:
2568:
2565:
2562:
2559:
2556:
2546:
2531:
2526:
2522:
2516:
2512:
2504:
2501:
2496:
2491:
2488:
2485:
2482:
2479:
2469:
2463:
2462:
2450:
2430:
2420:
2409:
2406:
2399:
2396:
2393:
2388:
2385:
2382:
2379:
2371:
2367:
2360:
2355:
2349:
2344:
2341:
2338:
2335:
2332:
2322:
2311:
2308:
2301:
2298:
2295:
2290:
2287:
2284:
2281:
2273:
2269:
2262:
2257:
2254:
2248:
2243:
2240:
2237:
2234:
2231:
2221:
2215:
2214:
2205:
2191:
2185:
2173:
2170:
2167:
2162:
2159:
2156:
2152:
2148:
2143:
2138:
2135:
2132:
2129:
2124:
2120:
2099:
2096:
2093:
2088:
2085:
2082:
2078:
2072:
2069:
2064:
2061:
2058:
2055:
2050:
2046:
2035:
2023:
2020:
2017:
2012:
2009:
2006:
2002:
1998:
1993:
1990:
1985:
1982:
1979:
1976:
1971:
1967:
1946:
1943:
1940:
1935:
1932:
1929:
1925:
1919:
1916:
1911:
1908:
1905:
1902:
1897:
1893:
1882:
1867:
1866:
1864:
1851:
1847:
1841:
1838:
1833:
1830:
1825:
1822:
1812:
1799:
1795:
1792:
1786:
1783:
1778:
1775:
1770:
1767:
1757:
1746:
1745:
1709:The area of a
1707:
1694:
1690:
1684:
1679:
1676:
1669:
1666:
1656:
1643:
1639:
1633:
1628:
1625:
1615:
1609:
1608:
1585:
1574:
1569:
1564:
1561:
1551:
1540:
1535:
1532:
1527:
1524:
1514:
1510:
1509:
1471:
1451:
1448:
1434:
1414:
1411:
1397:
1377:
1376:
1373:
1365:
1359:
1325:
1324:
1317:
1270:
1012:
1009:
1006:
1003:
968:
965:
962:
959:
951:
936:
935:
932:
929:
926:
860:Leonhard Euler
851:mathematician
772:
701:
695:
649:compass points
630:protractor".
601:
598:
576:
540:
537:
507:plenus angulus
497:
494:
489:
486:
441:
438:
406:
371:
368:
346:straight angle
342:winding number
263:by a complete
236:
235:
229:
220:
219:
213:
204:
203:
178:
169:
168:
144:
135:
134:
131:
130:
125:
118:
117:
113:
112:
109:
105:
104:
99:
95:
94:
90:
89:
81:
80:
72:
71:
61:
60:
38:
36:
29:
15:
9:
6:
4:
3:
2:
7603:
7592:
7589:
7587:
7584:
7582:
7579:
7577:
7574:
7573:
7571:
7562:
7561:
7557:
7556:
7537:
7533:
7527:
7512:
7508:
7502:
7500:
7493:
7483:
7479:
7472:
7465:
7459:
7452:
7451:
7444:
7437:
7426:
7422:
7416:
7414:
7412:
7404:
7400:
7393:
7382:
7378:
7374:
7370:
7366:
7362:
7358:
7357:Math Horizons
7351:
7344:
7326:
7319:
7312:
7304:
7300:
7296:
7292:
7287:
7282:
7278:
7274:
7267:
7259:
7255:
7249:
7241:
7237:
7231:
7223:
7222:
7217:
7210:
7202:
7198:
7192:
7184:
7180:
7173:
7165:
7161:
7155:
7147:
7143:
7137:
7122:
7118:
7114:
7108:
7093:
7089:
7085:
7079:
7064:
7060:
7056:
7050:
7035:
7031:
7025:
7010:
7006:
7002:
6996:
6981:
6977:
6973:
6966:
6951:
6947:
6943:
6937:
6922:
6918:
6914:
6908:
6893:
6889:
6888:
6883:
6876:
6861:
6857:
6853:
6849:
6845:
6839:
6831:
6827:
6823:
6819:
6815:
6812:. Interview.
6811:
6810:
6809:New Scientist
6802:
6784:
6777:
6770:
6756:
6752:
6748:
6744:
6740:
6736:
6732:
6726:
6712:
6708:
6704:
6700:
6696:
6690:
6675:on 2023-07-18
6671:
6664:
6657:
6642:
6641:Physics World
6638:
6631:
6613:
6609:
6605:
6601:
6597:
6593:
6589:
6585:
6584:
6576:
6575:"Pi is Wrong"
6569:
6567:
6551:
6550:
6542:
6534:
6530:
6529:
6524:
6518:
6503:
6499:
6493:
6486:
6475:
6474:
6466:
6458:
6452:
6437:
6433:
6429:
6428:
6420:
6412:
6407: : "Let
6406:
6402:
6399:
6395:
6392:
6384:
6380:
6376:
6369:
6362:
6354:
6350:
6346:
6342:
6338:
6334:
6327:
6320:
6316:
6315:
6307:
6296:
6292:
6289:
6285:
6268:
6264:
6260:
6256:
6249:
6242:
6234:
6230:
6226:
6219:
6211:
6207:
6198:Reprinted in
6196:
6191:
6190:
6185:
6184:
6179:
6174:
6170:
6152:
6149:
6146:
6139:
6136:
6122:
6118:
6114:
6108:
6100:
6096:
6092:
6080:
6077:
6071:
6057:
6053:
6049:
6043:
6035:
6031:
6027:
6015:
6012:
6006:
5994:
5991:
5985:
5979:
5976:
5961:
5957:
5953:
5949:
5945:
5939:
5935:
5931:
5930:
5925:
5919:
5911:
5905:
5901:
5897:
5892:
5891:
5882:
5874:
5870:
5869:
5864:
5858:
5843:
5839:
5835:
5829:
5815:on 2008-06-28
5814:
5810:
5808:
5803:
5797:
5789:
5785:
5784:
5776:
5768:
5764:
5761:(in German).
5760:
5759:
5754:
5747:
5739:
5735:
5731:
5727:
5726:
5718:
5703:
5699:
5695:
5689:
5685:
5681:
5677:
5673:
5669:
5662:
5660:
5650:
5646:
5642:
5638:
5634:
5629:
5628:
5622:
5616:
5614:
5606:
5604:
5590:
5586:
5580:
5573:
5572:
5564:
5557:
5555:
5541:
5537:
5531:
5524:
5523:
5515:
5508:
5506:
5502:
5489:
5485:
5481:
5474:
5459:
5455:
5451:
5444:
5429:
5425:
5421:
5414:
5399:
5395:
5391:
5387:
5381:
5366:
5362:
5356:
5341:
5337:
5331:
5316:
5310:
5306:
5302:
5298:
5294:
5293:
5285:
5270:
5264:
5260:
5256:
5252:
5251:
5243:
5229:
5225:
5221:
5220:
5214:
5206:
5204:
5189:on 2013-07-13
5188:
5184:
5183:
5178:
5172:
5170:
5154:
5150:
5143:
5141:
5121:
5117:
5110:
5109:
5102:
5088:
5082:
5078:
5074:
5073:
5065:
5061:
5045:
5036:
5027:
5018:
5009:
5005:
4995:
4992:
4990:
4987:
4985:
4984:
4980:
4978:
4977:Unit interval
4975:
4972:
4967:
4961:
4957:
4954:
4952:
4949:
4947:
4944:
4942:
4939:
4936:
4932:
4929:
4927:
4924:
4923:
4912:
4909:
4907:
4904:
4902:
4899:
4898:
4894:
4891:
4889:
4886:
4884:
4881:
4880:
4877:
4875:
4873:
4869:
4866:
4864:
4861:
4860:
4856:
4853:
4851:
4848:
4846:
4843:
4842:
4838:
4835:
4833:
4829:
4826:
4824:
4821:
4820:
4816:
4813:
4811:
4808:
4806:
4803:
4802:
4798:
4795:
4793:
4790:
4788:
4785:
4784:
4780:
4777:
4775:
4772:
4770:
4767:
4766:
4762:
4759:
4757:
4754:
4752:
4749:
4748:
4744:
4741:
4739:
4736:
4734:
4731:
4730:
4726:
4723:
4721:
4717:
4714:
4712:
4708:
4705:
4704:
4700:
4698:First Version
4697:
4694:
4691:
4690:
4687:
4678:
4676:
4675:
4670:
4666:
4662:
4653:
4647:
4645:
4638:
4634:
4631:
4628:
4626:
4622:
4621:
4616:
4612:
4608:
4605:
4602:
4598:
4593:
4590:
4588:
4587:
4582:
4581:
4576:
4575:
4570:
4566:
4544:
4534:
4523:
4520:
4513:
4512:
4511:
4505:
4501:
4496:
4494:
4493:
4459:
4453:
4445:
4440:
4437:
4430:
4429:
4428:
4426:
4422:
4417:
4415:
4411:
4405:
4403:
4376:
4373:
4369:
4364:
4361:
4354:
4353:
4352:
4350:
4345:
4343:
4339:
4335:
4334:
4329:
4325:
4316:
4313:
4311:
4307:
4304:
4301:
4299:
4295:
4292:
4289:
4283:
4279:
4273:
4268:
4265:
4261:In the ISQ/SI
4258:
4250:
4247:
4240:
4237:
4234:
4233:
4229:
4226:
4205:
4187:
4169:
4168:
4164:
4161:
4155:
4137:
4119:
4118:
4114:
4111:
4090:
4072:
4054:
4053:
4032:
4029:
4008:
3990:
3972:
3971:
3967:
3964:
3944:
3926:
3908:
3907:
3903:
3900:
3879:
3861:
3843:
3842:
3821:
3818:
3798:
3780:
3762:
3761:
3754:
3748:
3724:
3723:
3719:
3716:
3696:
3678:
3660:
3659:
3655:
3652:
3632:
3614:
3596:
3595:
3574:
3571:
3551:
3533:
3515:
3514:
3510:
3507:
3487:
3469:
3451:
3450:
3429:
3426:
3406:
3388:
3370:
3369:
3348:
3345:
3325:
3307:
3289:
3288:
3284:
3281:
3275:
3274:
3271:
3268:
3266:
3263:
3261:
3256:
3253:
3252:
3246:
3244:
3240:
3236:
3215:
3204:
3198:
3194:
3190:
3189:circumference
3185:
3172:
3158:
3153:
3148:
3145:
3138:
3124:
3119:
3116:
3111:
3108:
3101:
3099:
3096:
3095:
3091:
3086:
3082:
3063:
3058:
3055:
3048:
3029:
3026:
3021:
3018:
3011:
3009:
3006:
3005:
3002:
2986:
2980:
2975:
2969:
2966:
2963:
2960:
2955:
2949:
2944:
2938:
2935:
2932:
2925:
2922:
2917:
2912:
2906:
2898:
2882:
2876:
2871:
2866:
2858:
2855:
2852:
2849:
2844:
2838:
2833:
2828:
2820:
2817:
2814:
2807:
2804:
2799:
2794:
2791:
2785:
2777:
2775:
2769:
2768:
2765:
2749:
2744:
2739:
2736:
2731:
2724:
2719:
2712:
2709:
2706:
2699:
2683:
2678:
2673:
2670:
2665:
2658:
2653:
2650:
2643:
2640:
2637:
2630:
2628:
2625:
2624:
2621:
2603:
2598:
2594:
2588:
2584:
2576:
2571:
2566:
2560:
2554:
2547:
2529:
2524:
2520:
2514:
2510:
2502:
2499:
2494:
2489:
2483:
2477:
2470:
2468:
2465:
2464:
2448:
2428:
2421:
2407:
2404:
2397:
2394:
2391:
2383:
2377:
2369:
2365:
2358:
2353:
2347:
2342:
2336:
2330:
2323:
2309:
2306:
2299:
2296:
2293:
2285:
2279:
2271:
2267:
2260:
2255:
2252:
2246:
2241:
2235:
2229:
2222:
2220:
2217:
2216:
2211:
2204:
2197:
2190:
2186:
2184:
2168:
2160:
2157:
2154:
2150:
2146:
2141:
2136:
2130:
2122:
2118:
2094:
2086:
2083:
2080:
2076:
2070:
2067:
2062:
2056:
2048:
2044:
2036:
2034:
2018:
2010:
2007:
2004:
2000:
1996:
1991:
1988:
1983:
1977:
1969:
1965:
1941:
1933:
1930:
1927:
1923:
1917:
1914:
1909:
1903:
1895:
1891:
1883:
1881:
1878:
1869:
1868:
1865:
1849:
1845:
1839:
1836:
1831:
1828:
1823:
1820:
1813:
1797:
1793:
1790:
1784:
1781:
1776:
1773:
1768:
1765:
1758:
1755:
1748:
1747:
1742:
1723:
1717:
1712:
1708:
1692:
1688:
1682:
1677:
1674:
1667:
1664:
1657:
1641:
1637:
1631:
1626:
1623:
1616:
1614:
1611:
1610:
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1590:
1586:
1572:
1567:
1562:
1559:
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1533:
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1515:
1512:
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1446:
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1379:
1378:
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1366:
1360:
1357:
1356:
1351:
1349:
1348:
1335:
1331:
1318:
1315:
1311:
1307:
1306:UE Blueprints
1303:
1299:
1295:
1291:
1287:
1283:
1279:
1272:The constant
1271:
1267:
1262:
1258:
1257:
1256:
1253:
1247:
1245:
1242:arising from
1224:
1204:
1193:
1186:
1182:
1177:
1171:
1166:
1165:Tau Manifesto
1152:
1141:begin with a
1140:
1132:
1113:
1092:
1065:
1061:
1056:
1052:
1051:Michael Hartl
1047:
1037:
1029:
1024:
1010:
1007:
1004:
1001:
993:
989:
985:
980:
966:
963:
960:
957:
949:
933:
930:
927:
920:
919:
918:
917:, including:
908:
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890:
886:
884:
879:
878:
865:
861:
856:
854:
853:William Jones
850:
837:
829:
820:
816:
815:circumference
812:
803:
795:
786:
785:David Gregory
770:
761:
759:
755:
754:circumference
739:
731:
720:
714:
709:
704:
700:
694:
684:
664:
660:
659:
658:binary radian
654:
653:binary degree
650:
646:
642:
640:
636:
631:
629:
625:
621:
617:
607:
597:
595:
594:
590:multiples of
582:
574:
570:
566:
562:
558:
554:
550:
549:HP Prime
546:
545:HP 39gII
536:
534:
530:
525:
518:
513:
508:
503:
493:
485:
482:
476:
472:
468:
467:
462:
458:
453:
439:
436:
428:
424:
423:circumference
420:
404:
396:
395:Michael Hartl
392:
389:
384:representing
369:
366:
357:
355:
351:
347:
343:
339:
335:
331:
330:
325:
324:
319:
315:
311:
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303:
299:
295:
291:
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283:
279:
274:
273:
266:
262:
259:
255:
251:
247:
243:
230:
228:
221:
214:
212:
205:
201:... mrad
187:
179:
177:
170:
153:
145:
143:
136:
132:
129:
126:
124:
120:
119:
114:
110:
106:
103:
100:
96:
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78:
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52:
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44:
43:
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28:
27:
22:
7559:
7539:. Retrieved
7535:
7526:
7515:. Retrieved
7513:. 2001-08-31
7510:
7485:. Retrieved
7471:
7449:
7443:
7429:. Retrieved
7392:
7360:
7356:
7343:
7332:. Retrieved
7311:
7276:
7272:
7266:
7257:
7248:
7239:
7230:
7219:
7209:
7200:
7197:"Math class"
7191:
7182:
7177:Darcy, Joe.
7172:
7163:
7154:
7145:
7136:
7125:. Retrieved
7116:
7107:
7096:. Retrieved
7087:
7078:
7067:. Retrieved
7058:
7049:
7038:. Retrieved
7024:
7013:. Retrieved
7004:
6995:
6984:. Retrieved
6975:
6965:
6954:. Retrieved
6945:
6936:
6925:. Retrieved
6916:
6907:
6896:. Retrieved
6885:
6875:
6864:. Retrieved
6851:
6838:
6816:(2794): 23.
6813:
6807:
6801:
6790:. Retrieved
6769:
6758:. Retrieved
6738:
6725:
6714:. Retrieved
6702:
6689:
6677:. Retrieved
6670:the original
6656:
6645:. Retrieved
6640:
6630:
6619:. Retrieved
6587:
6581:
6554:. Retrieved
6548:
6541:
6532:
6527:
6517:
6506:. Retrieved
6504:. 2024-03-14
6501:
6492:
6477:
6472:
6465:
6440:. Retrieved
6426:
6419:
6410:
6390:
6386:
6378:
6368:
6356:
6339:(3): 75–84.
6336:
6332:
6322:
6313:
6306:
6280:
6274:. Retrieved
6258:
6257:(in Latin).
6254:
6241:
6233:the original
6228:
6218:
6209:
6187:
6181:
6177:
6172:
6168:
5959:
5955:
5951:
5947:
5943:
5941:
5928:
5918:
5889:
5881:
5867:
5857:
5846:. Retrieved
5828:
5817:. Retrieved
5813:the original
5805:
5796:
5782:
5775:
5762:
5756:
5746:
5729:
5723:
5717:
5705:. Retrieved
5671:
5626:
5596:. Retrieved
5570:
5563:
5547:. Retrieved
5521:
5514:
5498:
5492:. Retrieved
5483:
5473:
5462:. Retrieved
5453:
5443:
5432:. Retrieved
5423:
5413:
5402:. Retrieved
5389:
5380:
5369:. Retrieved
5355:
5344:. Retrieved
5330:
5319:. Retrieved
5291:
5284:
5273:. Retrieved
5249:
5242:
5231:. Retrieved
5217:
5191:. Retrieved
5187:the original
5180:
5157:. Retrieved
5127:. Retrieved
5107:
5101:
5090:. Retrieved
5071:
5064:
5044:
5035:
5026:
5017:
5008:
4981:
4965:
4933:(modern) or
4906:std.math.tau
4684:
4672:
4658:
4629:
4624:
4600:Unit of
4584:
4578:
4572:
4562:
4497:
4490:
4484:
4424:
4418:
4407:
4399:
4348:
4347:
4341:
4332:
4331:
4327:
4321:
4298:SI unit
4290:
4264:
4256:
3254:
3213:
3209:
3202:
3084:
2209:
2202:
2195:
2188:
2110:
1957:
1876:
1740:
1721:
1715:
1603:
1599:
1593:
1478:
1396:of a circle
1369:
1342:
1333:
1329:
1326:
1265:
1261:Khan Academy
1251:
1248:
1222:
1202:
1191:
1184:
1175:
1169:
1164:
1138:
1130:
1111:
1090:
1063:
1059:
1048:
1025:
981:
937:
909:
892:
881:
875:
863:
857:
835:
827:
801:
793:
762:
744:
703:
698:
662:
656:
652:
643:
632:
620:21′ 36″
609:
600:Subdivisions
588:
573:HP 40gs
569:HP 39gs
565:HP 49g+
561:hp 39g+
542:
499:
491:
488:Unit symbols
474:
465:
464:
454:
387:
358:
338:transformers
327:
321:
313:
309:
305:
304:) or to one
301:
297:
293:
290:angular unit
284:or 400
271:
249:
245:
241:
239:
185:
176:milliradians
166:... rad
151:
127:
122:
98:Unit of
64:
55:
40:
7273:Kybernetika
6731:Mann, Steve
6695:Mann, Steve
6183:John Machin
5952:Curve Lines
5712:(736 pages)
5653:(320 pages)
5621:Hoyle, Fred
5607:(271 pages)
5558:(314 pages)
5505:conversions
5257:, reprint:
4960:solid angle
4926:Ampere-turn
4695:Identifiers
4623:1 rev
4583:(cps), and
4410:ISO 80000-3
4340:defined as
4276:Other names
3199:is one) is
3193:unit circle
1316:, and Odin.
1244:integration
1133:, and both
889:unit circle
745:The number
581:WP 43S
557:HP 50g
539:Calculators
515: [
393:. In 2010,
350:right angle
280:, 360
254:plane angle
102:Plane angle
7591:1 (number)
7570:Categories
7541:2023-05-12
7517:2023-04-25
7487:2023-07-17
7438:(11 pages)
7431:2019-10-23
7334:2018-09-20
7286:1601.05179
7214:John-H-K.
7146:Godot Docs
7127:2020-10-09
7098:2019-08-05
7069:2019-08-05
7059:Processing
7040:2019-08-05
7015:2019-08-05
6986:2019-08-05
6976:Python.org
6956:2023-03-21
6927:2020-12-19
6898:2015-03-20
6866:2019-08-05
6792:2019-08-05
6760:2023-07-18
6716:2023-07-18
6684:(18 pages)
6679:2023-07-18
6647:2024-08-03
6621:2019-08-05
6556:2024-07-24
6508:2024-03-26
6442:2017-10-15
6283:I : π
6276:2017-10-15
6189:Van Ceulen
5898:. p.
5848:2019-08-05
5819:2019-08-05
5707:2019-08-06
5598:2019-08-05
5549:2019-08-05
5494:2019-08-05
5464:2019-08-07
5434:2019-08-05
5404:2013-01-01
5371:2019-08-06
5346:2019-08-06
5321:2015-08-14
5275:2015-08-14
5233:2020-05-21
5193:2019-08-05
5159:2013-09-14
5129:2023-07-18
5092:2023-04-25
5056:References
4971:steradians
4823:Processing
4644:Base units
4595:Revolution
4485:where {𝜑}
4034:133
1874:-ball and
1290:Processing
706:See also:
635:Fred Hoyle
628:percentage
624:protractor
604:See also:
524:Vollwinkel
512:DIN 1301-1
326:(cps) and
306:revolution
189: mrad
121:1 tr
7396:Sequence
7377:126179022
7363:(4): 34.
7303:119126029
6755:189926593
6608:120965049
6478:Si autem
6451:cite book
6409:1 :
6389:1 :
6229:veling.nl
6144:&
6137:−
6132:¯
6109:−
6067:¯
6044:−
6007:−
6002:¯
5986:−
5865:(1989) .
5627:Astronomy
5484:HP Museum
5424:HP Museum
5228:0099-9660
5077:CRC Press
4778:Godot 3.0
4460:φ
4446:φ
4381: rad
4377:π
4370:φ
4310:Dimension
3823:66
3576:33
3431:16
3241:, or 400
3154:τ
3146:ω
3120:π
3109:ω
3069:ℏ
3064:τ
3035:ℏ
3030:π
2981:τ
2970:
2950:τ
2939:
2913:τ
2877:π
2859:
2839:π
2821:
2795:π
2720:τ
2713:∼
2654:π
2644:∼
2589:−
2577:τ
2555:φ
2515:−
2503:π
2478:φ
2429:γ
2395:−
2370:γ
2366:∮
2354:τ
2297:−
2272:γ
2268:∮
2256:π
2158:−
2142:τ
2084:−
2008:−
1992:π
1931:−
1846:τ
1840:
1794:π
1785:
1713:of angle
1683:τ
1632:π
1591:of angle
1568:τ
1534:π
1458: rad
1447:τ
1421: rad
1410:π
1049:In 2010,
1011:π
1002:ψ
982:In 2008,
967:π
958:π
950:π
880:and 1748
877:Mechanica
821:had used
811:perimeter
771:π
440:π
405:τ
370:π
261:subtended
155: rad
84:rotations
7381:Archived
7325:Archived
7121:Archived
7092:Archived
7063:Archived
7034:Archived
7009:Archived
6980:Archived
6950:Archived
6921:Archived
6892:Archived
6860:Archived
6783:Archived
6612:Archived
6525:(1746).
6436:Archived
6401:Archived
6387:Denotet
6357:Letting
6291:Archived
6267:Archived
5926:(1706).
5842:Archived
5702:88-25858
5641:62065943
5589:Archived
5540:Archived
5488:Archived
5458:Archived
5428:Archived
5398:Archived
5365:Archived
5340:Archived
5153:Archived
5120:Archived
5118:. 2016.
4920:See also
4850:math.tau
4792:Math.TAU
4769:GDScript
4692:Language
4604:Rotation
4330:(symbol
4328:rotation
4303:Unitless
4270:Rotation
3350:5
3270:Gradians
3243:gradians
3217:(≈
1302:GDScript
862:'s 1727
555:for the
502:DIN 1315
466:rotation
308:(symbol
296:(symbol
288:. As an
286:gradians
244:(symbol
227:gradians
7536:iso.org
7403:A019692
7401::
6852:cnn.com
6818:Bibcode
6711:6462220
6594:: 7–8.
6353:2973441
6261:: 351.
6176:. This
5944:Lengths
5649:7419446
4937:(older)
4760:Curtiss
4733:Crystal
4589:(rpm).
4416:(SI).
4336:) is a
4326:(ISQ),
4322:In the
4238:𝜏 rad
4235:1 turn
4222:
4207:
4201:
4189:
4183:
4171:
4151:
4139:
4133:
4121:
4107:
4092:
4086:
4074:
4068:
4056:
4049:
4025:
4010:
4004:
3992:
3986:
3974:
3960:
3946:
3940:
3928:
3922:
3910:
3896:
3881:
3875:
3863:
3857:
3845:
3838:
3814:
3800:
3794:
3782:
3776:
3764:
3741:
3726:
3712:
3698:
3692:
3680:
3674:
3662:
3648:
3634:
3628:
3616:
3610:
3598:
3591:
3567:
3553:
3547:
3535:
3529:
3517:
3503:
3489:
3483:
3471:
3465:
3453:
3446:
3422:
3408:
3402:
3390:
3384:
3372:
3365:
3341:
3327:
3321:
3309:
3303:
3291:
3276:0 turn
3265:Degrees
3260:Radians
3239:degrees
3235:radians
3195:(whose
3191:of the
3088:is the
1738:
1726:
1505:
1493:
1489:
1475:
1394:
1382:
1358:Formula
1240:
1228:
1219:
1207:
1122:
1107:
1101:
1086:
1081:
1069:
840:
824:
806:
790:
756:to its
679:
667:
529:SI unit
463:called
455:In the
425:to its
336:(e.g.,
282:degrees
278:radians
211:degrees
142:radians
51:Discuss
7460:
7427:. 2019
7375:
7301:
7221:GitHub
7084:"math"
6753:
6709:
6606:
6351:
6178:Series
5960:Circle
5956:Planes
5906:
5700:
5690:
5647:
5639:
5581:
5532:
5501:WP 34S
5311:
5265:
5226:
5083:
4969:
4958:– the
4892:1.47.0
4845:Python
4832:TWO_PI
4814:0.14.0
4751:Eiffel
4742:0.36.0
4674:period
4625:in ...
4610:Symbol
4577:(Hz),
3752:57.3°
3746:1 rad
3508:22.5°
3279:0 rad
3237:, 360
3197:radius
1711:sector
1491:rad =
1375:Notes
1367:Using
1361:Using
1321:τ
1282:Python
1274:τ
1266:τ
1252:τ
1198:τ
1176:π
1170:τ
1157:τ
1135:τ
1127:τ
1064:π
1060:τ
912:𝜏 = 2
758:radius
723:τ
665:), is
571:, and
553:newRPL
427:radius
348:and a
276:
265:circle
123:in ...
108:Symbol
47:merged
7586:Angle
7454:(PDF)
7384:(PDF)
7373:S2CID
7353:(PDF)
7328:(PDF)
7321:(PDF)
7299:S2CID
7281:arXiv
7055:"TAU"
6786:(PDF)
6779:(PDF)
6751:S2CID
6707:S2CID
6673:(PDF)
6666:(PDF)
6615:(PDF)
6604:S2CID
6578:(PDF)
6349:JSTOR
6270:(PDF)
6251:(PDF)
6193:'
5948:Areas
5946:, or
5807:ooPIC
5592:(PDF)
5575:(PDF)
5543:(PDF)
5526:(PDF)
5123:(PDF)
5112:(PDF)
5000:Notes
4931:Hertz
4913:2019
4910:0.6.0
4895:2020
4857:2016
4839:2013
4817:2016
4799:2022
4781:2018
4745:2021
4727:2020
4574:hertz
4502:(the
4248:360°
4227:270°
4185:turn
4162:180°
4135:turn
4112:144°
4070:turn
4030:120°
3988:turn
3924:turn
3859:turn
3778:turn
3758:63.7
3743:turn
3676:turn
3612:turn
3531:turn
3467:turn
3386:turn
3305:turn
3255:Turns
3219:6.283
2212:) = 2
2198:) = 1
1028:theta
925:1990)
849:Welsh
787:used
616:angle
519:]
481:below
479:(See
471:ratio
294:cycle
159:6.283
7458:ISBN
7399:OEIS
6498:"Pi"
6457:link
6432:E101
6383:E015
6319:E858
6263:E007
5904:ISBN
5698:LCCN
5688:ISBN
5645:OCLC
5637:LCCN
5579:ISBN
5530:ISBN
5309:ISBN
5263:ISBN
5224:ISSN
5081:ISBN
4883:Rust
4870:and
4863:Raku
4830:and
4787:Java
4718:and
4711:.NET
4571:are
4251:400
4245:rad
4230:300
4224:rad
4203:rad
4165:200
4159:rad
4153:rad
4115:160
4109:rad
4088:rad
4027:rad
4006:rad
3968:100
3965:90°
3962:rad
3942:rad
3901:72°
3898:rad
3877:rad
3819:60°
3816:rad
3796:rad
3717:45°
3714:rad
3694:rad
3653:36°
3650:rad
3630:rad
3572:30°
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