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#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

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,818

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

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#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?

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,818

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

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#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)=⏀

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,490

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.

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