What does the polar equation $r=k\theta$ represent? (Fibonacci Sequence, Golden Ratio, Archimedes' Spiral, or Torus)

Question

Using the polar coordinate system, $r$ increases directly with $\theta$. In other words, $r=k\theta$. Which of the following shapes is constructed?

A) Fibonacci Sequence

B) Golden Ratio

C) Archimedes' Spiral

D) Torus

After a bit of research, I'm inconclusive about which shape is constructed. Anybody know what shape it is given the aforementioned information? Appreciate it guys

Answer 1

• A) The Fibonacci sequence is sequence of integers, not a geometrical curve.
• B) The golden ratio is an algebraic number $\varphi=\frac{1+\sqrt 5}2$, not a geometrical curve.
• D) A torus is a three-dimensional geometrical object, not a curve.

Even without knowing the name of the curve $r=k\theta$, you could figure out that the answer is C.

Answer 2

Are you joking?

This couldn't be a serious question.

You should draw the shape constructed. Or you can at least think about how it may look like.

Does the line look like a sequence of numbers?

Does the line look like a number?

Does the line look like a line?

Does the line look like a 3 dimensional body or surface?

By answering these questions you'll get the final answer.

Answer 3

A radius that varies as it rotates builds a... ? Obviously not a circle, since the radius of the latter is constant... but something round or circular nevertheless, right ? Now, of all your $4$ choices, which one comes closest to such a shape ? :-)