quadratrix of hippias viet to, jackie gomez, deon nguyen
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Quadratrix of Hippias
Viet To, Jackie Gomez, Deon Nguyen
A B
C D
Start with a square of unit length and vertices A, B, C, and D.
A B
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.
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
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.
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
A B
C D
The curve is called the Quadratrix of Hippias.
The trisection of any angle
M
NO
Start with angle MON to trisect.
The quadratrix could be used to trisect an angle.
M
NO
T
The trisection of any angle
Draw the Quadratrix.
The trisection of any angle
M
NO
T
S
Drop the vertical from the point of intersection T to the horizontal at S.
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.
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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