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#1 2008-06-11 02:42:06

Daniel123
Member
Registered: 2007-05-23
Posts: 663

Wierd graph

Plot of the Daniel Curve

Zoom in and out smile

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

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#2 2008-06-11 02:49:18

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.

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#3 2008-06-11 02:53:38

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 smile

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

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#4 2008-06-11 03:36:50

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


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

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#5 2008-06-11 07:50:41

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! smile

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

A logarithm is just a misspelled algorithm.

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#6 2008-06-11 15:10:24

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)


igloo myrtilles fourmis

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#7 2008-06-11 20:54:35

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)


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

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#8 2008-06-11 22:51:56

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Wierd graph

You spelled “weird” incorrectly.

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#9 2008-06-11 23:46:56

Daniel123
Member
Registered: 2007-05-23
Posts: 663

Re: Wierd graph

JaneFairfax wrote:

You spelled “weird” incorrectly.

'twas a typing mistake. I can spel.

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#10 2008-06-12 09:31:57

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: Wierd graph

Picky picky, Jane! tongue

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!


A logarithm is just a misspelled algorithm.

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