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to three similar right triangles, each having as vertices the point where the perpendicular touches the semicircle and two of the three endpoints of the segments of lengths
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to their neighbours, and to the x-axis at these points. Semicircles joining adjacent points on the x-axis pass through the points of contact at right angles.
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of a rectangle. The side length of the square is the geometric mean of the side lengths of the rectangle. More generally, it is used as a
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in a general method for transforming any polygonal shape into a similar copy of itself with the area of any other given polygonal shape.
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The construction of the geometric mean can be used to transform any rectangle into a square of the same area, a problem called the
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means of two lengths using straight-edge and compass. For a semicircle with a diameter of
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from 1 to 9. Each semicircle intersects its corresponding circles at right angles.
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hover over a circle or curve to highlight it and its terms.
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If it is entirely concave from above, the equation is
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