Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

Login

Username

Password

Not registered yet?

#1 2013-09-23 01:54:13

prathima
Member

Offline

logarithmic spiral

in polar coordinates, the logarithmic spiral is given by r=ae^(bθ)
how find θ and how to draw logarithmic spiral

#2 2013-09-23 01:59:39

anonimnystefy
Real Member

Online

Re: logarithmic spiral

θ is just a variable, similar to x in y=x^2.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#3 2013-09-23 02:07:06

prathima
Member

Offline

Re: logarithmic spiral

is there any particular formula?
without using any formula how to find θ
as radius varies  θ also varies right?

#4 2013-09-23 02:14:14

anonimnystefy
Real Member

Online

Re: logarithmic spiral

The way it is done is, you take values for θ and calculate the value of r you get.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#5 2013-09-23 02:26:27

prathima
Member

Offline

Re: logarithmic spiral

The spiral has the property that the angle φ between the tangent and radial line at the point (r, \theta) is constant. This property can be expressed in differential geometric terms as


arc cos[(r(θ), r'(θ)/||r(θ)||*||r'(θ)]=arctan(1/b)=⏀

#6 2013-09-23 03:16:45

bobbym
Administrator

Offline

Re: logarithmic spiral

Hi;

Theta is an independent variable and r is the dependent one.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Board footer

Powered by FluxBB