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

You are not logged in.

#1 2013-09-22 03:54:13

prathima
Member
Registered: 2013-09-19
Posts: 33

logarithmic spiral

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

Offline

#2 2013-09-22 03:59:39

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: logarithmic spiral

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


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#3 2013-09-22 04:07:06

prathima
Member
Registered: 2013-09-19
Posts: 33

Re: logarithmic spiral

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

Offline

#4 2013-09-22 04:14:14

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: logarithmic spiral

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


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#5 2013-09-22 04:26:27

prathima
Member
Registered: 2013-09-19
Posts: 33

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)=⏀

Offline

#6 2013-09-22 05:16:45

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,316

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

Board footer

Powered by FluxBB