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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: 15,918

### 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
The knowledge of some things as a function of age is a delta function.

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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: 15,918

### 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
The knowledge of some things as a function of age is a delta function.

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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
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,764

### 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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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