Math Is Fun Forum

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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: logarithmic spiral

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

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“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.

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?

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: logarithmic spiral

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

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“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.

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)=⏀

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: logarithmic spiral

Hi;

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

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