Macchine Matematiche

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Angle trisection

 

Compass-and-straightedge construction, also known as ruler-and-compass contruction, is a subject of very high mathematical and historic interest. Despite mathematicians from the ancient Greece knew other instruments, they decided to apply the restriction to use these two instruments only but, whether many attempts were made, unfortunately no contructions were found to solve problems such as doubling the cube, trisecting the angle or squaring the circle.

By letting the students use and examine several instruments desingned throug about 2000 years of history going from Nicomedes to Kempe, this hands-on-lab offers the opportunity to familiarise with the problem of the angle trisection.

Two are the kinds of instruments provided to the students: trisectors, which directly divide the given angle in three equal parts (two rods are positioned so to overlap the angle to be trisected, and the remaning two rods form an angle which is the third part of the given one), or tools that draw curves (trisectrexis) that properly related to the given angle, enable to divide it in three equal parts.

Hands-on activity presentation (ita)

Guiding forms

Trisectors
Pascal's trisector (ita)

Animation

Cartesius' trisector (ita)

Animation

Tomahawk (ita)


Ceva's trisector (ita)

Animation

Ball's trisector (ita)
Animation
Kempe's trisector (ita)
Animation
Trisectrixes
Conchoide of Nicomedes (ita)
Animation
Pascal's limacon (ita)
Animation
Archimedean spiral (ita)
 

Hystorical sources

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