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Quadratrix of Hippias Viet To, Jackie Gomez, Deon Nguyen
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AB C D Start with a square of unit length and vertices A, B, C, and D.
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AB C D The top horizontal line – the line AB – starts moving down with uniform velocity until it reach the bottom – line CD. At the same time, the left vertical line – line AC – starts rotating (anchored at point C) with uniform velocity until it reach the bottom – line CD.
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AB C D
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AB C D We are interested in the point of intersections of line AB and line AC. Connect all the points of intersection to trace a curve.
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AB C D The curve is called the Quadratrix of Hippias.
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The trisection of any angle M NO Start with angle MON to trisect. The quadratrix could be used to trisect an angle.
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M NO T The trisection of any angle Draw the Quadratrix.
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The trisection of any angle M NO T S Drop the vertical from the point of intersection T to the horizontal at S.
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The trisection of any angle M NO T S H Find the point H that trisects the segment ST, and draw the horizontal at H.
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The trisection of any angle M NO T H S P Draw the line from O to the point P where the quadratrix intersects the horizontal line drawn at H.
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