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Seven math curves

SOLVED
Emerald III

Seven math curves

1 ACCEPTED SOLUTION

Accepted Solutions

Re: Seven math curves

83 REPLIES 83

Re: Seven math curves

Why not stay with the four basic operations and replace one of the points by a straight line?!

We have (with a=distance from the focal point and b=distance from the straight line):

a+b=const -> parabola

a-b=const -> parabola

a/b=const -> conic (a/b>1: hyperbola, a/b=1: parabola, a/b <1 ellipse)

a*b=const. -> ???

Re: Seven math curves

Seven is one fine number - for not.

Re: Seven math curves

Why be content with seven when you can have eleven or more ?

As it looks you like playing around with that kind of curves and also have the time doing so, her some additional ideas.

Stay with simple sum and used weighted distances. Something like two "focal" points 2a+3b=const when a and b are the distances from the "focals".

Or use more than one focal point. What about a curve, where the sum of the distances from three points is constant.

Regards

WE

Re: Seven math curves

As a starter here an animation demonstrating my last suggestion

Re: Seven math curves

Here is a second animation, varying the constant

But beside all of this we shall not forget, that all these gizmos make only sense, if for these new(?) curves interesting properties (a closed parametric representation, arc length, encloses area), be them mathematical or other, are found.


WE

Re: Seven math curves

Thanks, Werner.

One more thanks, that you not insert animation into your replies - now I am not in Moscow - I am on my dacha - not far from the place where Tchebyshev was born. Here Internet is very expensive.

See please Pafnuty Chebyshev - Wikipedia, the free encyclopedia

PS

Do you know how many built-in Mathcad functions has names based of persons.

Tcheb

rkfixed

J0

etc

Re: Seven math curves

And what about

a • b • c = const

or

a^b^c = const

Re: Seven math curves

1. black+blue

1-ellipse.png

Re: Seven math curves

2. |black-bleu|

2-hyperbola.png