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

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,359

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

is there any particular formula?

without using any formula how to find θ

as radius varies θ also varies right?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,359

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,480

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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