Involute Constructions: Square, Triangle, Pentagon

What is the first step to construct the involute of a saura?

How long is the side of the equilateral triangle in Problem 2?

What points are used to form the involute of the triangle?

What is the side length of the regular pentagon in Problem 3?

Which point is used as the center for the arc when constructing the involute of the pentagon?

The curve formed by joining the points D, P1, P2, P3, and P4 is called the involute of the ______.

What is the radius used for creating the arc centered at C when constructing the involute of the triangle?

Involute of a Saura

To construct the involute of a square, first construct an arc with center C and radius $CP_2$. This arc intersects the extended line DC at $P_3$.
Then, create an arc centered at D with radius $DP_3$ and intersecting the extended line AD at $P_4$.
The curve formed by joining the points D, $P_1$, $P_2$, $P_3$, $P_4$ is called the involute of the square, also known as the involute of the saura.

Involute of an Equilateral Triangle

Draw an equilateral triangle with a side of 20 mm.
Using B as the center and a radius of BA (20 mm), draw an arc that intersects the extended line CB at P.
Then, using C as the center and a radius of $CP_1$ (twice the side length), draw an arc intersecting the extended line AC at $P_2$.
Finally, with center A and radius $AP_2$, draw an arc intersecting the extended line BA at $P_3$.
The curve formed by joining points A, $P_1$, $P_2$, $P_3$ is the involute of the triangle.

Involute of a Regular Pentagon

Draw a regular pentagon with a side length of 25 mm.
Use A as the center and an arc with a radius AE = 25 mm.
Use B as the center and a radius BP, where P is the intersection of the arc and the extended line CB.

This quiz explores the construction of involutes for various geometric shapes such as squares, equilateral triangles, and regular pentagons. Participants will learn the step-by-step methods for drawing involutes, enhancing their understanding of geometric relationships and properties. Test your knowledge on these fascinating curves and their applications in geometry.