Math Is Fun Forum

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Wierd graph

Plot of the Daniel Curve

Zoom in and out

Last edited by Daniel123 (2008-06-11 02:44:28)

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Wierd graph

Looks like y = x is tangential to each of the little arches. I can't be bothered to check this analytically.

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Wierd graph

Plot the graph, alongside its negative, in polar coordinates with as many revolutions as you can, and zoom out

Last edited by Daniel123 (2008-06-11 02:54:28)

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Wierd graph

so y = x crosses your graph at x = 2kpi, and at each of these points, the gradient of your curve is 1, so y = x is a tangent to the curve on each of its sections

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The Beginning Of All Things To End.
The End Of All Things To Come.

mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: Wierd graph

by wrapping the cosine in absolute value, you can make the graph continuous!

ln(abs((cos(x))/(e^(-x))))

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A logarithm is just a misspelled algorithm.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Wierd graph

Is the y value undefined in the gaps?  Just wondering.
(I'm not analyzing details, but just wondered if it was the ln of a negative number)

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igloo myrtilles fourmis

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Wierd graph

It is john, the undefined areas of the graph are when cos(x) <= 0

the equation of the his graph can be rearranged more simply as x + ln(cos x)

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The Beginning Of All Things To End.
The End Of All Things To Come.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Wierd graph

You spelled “weird” incorrectly.

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Wierd graph

You spelled “weird” incorrectly.

'twas a typing mistake. I can spel.

mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: Wierd graph

Picky picky, Jane!

Anyway, it is fun to replace x in many functions with b*sin(a*x), as it must result in a repeating pattern.

Try graphing sin(pi*sin(x)) for instance!

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A logarithm is just a misspelled algorithm.