In polar coordinates, there are two kinds of spiral which are the Spiral of Archimedes and Logarithmic Spirals.
A spiral of Archimedes is the form r=aΘ+b and a logarithmic spiral is of the form r=ab^Θ. Am I right? But when I'm trying to graph these two spirals I cannot determine their differences because they are almost the same.

Can someone explain how they differ? Thank you.

Question

In polar coordinates, there are two kinds of spiral which are the Spiral of Archimedes and Logarithmic Spirals. 
A spiral of Archimedes is the form r=aΘ+b and a logarithmic spiral is of the form r=ab^Θ. Am I right? But when I'm trying to graph these two spirals I cannot determine their differences because they are almost the same. 

Can someone explain how they differ? Thank you.

kropot72 · Answer

According to Wikipedia: "The logarithmic spiral can be distinguished from the Archimedean spiral by the fact that the distances between the turnings of a logarithmic spiral increase in geometric progression, while in an Archimedean spiral these distances are constant." More information is at http://en.wikipedia.org/wiki/Logarithmic_spiral

sirm3d · Answer

if you graph them on the same polar plane, you'd be able to see the difference

anonymous · Answer

Maybe, because I graph it in 0 to 2Π only. I will try to graph it again in higher value.

sirm3d · Answer

green is logarithmic, blue is archimedes'

anonymous · Answer

Okay logarithmic spiral has wider graph than Archimedes, right? Thank you