Please tell me how we Sketch the Spiral of Archimedes r = a(theta), a>0
Please tell me with step by step..
Please explain me with all steps..

Plz tell me how we Sketch the Spiral of Archimedes r = a(theta), a>0
Plz tell me with step by step...?
Plz explain me with all steps...?


Visualization sometimes helps.


Imagine a wagon wheel with, say twelve spokes. Start at the centre (hub) and choose any spoke. Divide the chosen spoke into 12 equal parts. Start at the hub and work your way to the rim. Each notch will be equidistant. There are twelve spokes and one spoke will twelve notches.

Rotate the notched spoke through 360 degs. Each time the spoke passes over another spoke the radial arm (spoke) shortens by a twelfth. Also imagine that the slightly shortened arm leaves its notch on the spoke it passes over.

The first spoke it pass over leaves a notch 11/12 from the hub. The next spoke it passes over leaves a notch 10/12 from the hub and so on through 360 degs.

Join the notches with a string and you have your spiral.