# Arc Trisection & Square A= Circle A Impossible Construction

Given:

Define a geometric construction as an object that can be created using only a compass and a straightedge. Mathematicians have shown that it is not possible to:

1. Geometrically construct a square with an area equal to that of a given circle.

2. Use a geometric construction to trisect an arbitrary angle.

The proofs of these two theorems require abstract algebra.

Task:

Describe the mathematics used to solve each of these problems (you do not need to supply proofs).

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#### Solution Preview

The mathematics that you would use to develop these proofs would be:

1.)For the proof related to the area of the circle vs. the area of the square you would use the relationships that define area for both of these shapes and tie them together.

Pi*r^2 = s^2

This would ...

#### Solution Summary

It is impossible to create the trisection of an arc or the construction of a square with an area equal to a circle with classic construction techniques using only a straight edge and a compass. This solution explains in a mathematical way why it can't be done.