Equality of a Segment and an Arc in Archimedes's Spiral

move

2.8416

OT = 8.0747

arc POK = 8.0747

This Demonstration illustrates Proposition 20 of Archimedes's work On Spirals.

Let

P

be any point on the first turn of the spiral, and let

T

be the intersection of the tangent to the spiral at

P

, with the perpendicular to

OP

at

O

. Then

OT=arcPOK

.