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07-05-2016
02:42 PM

07-05-2016
02:42 PM

Re: Seven math curves

Werner Exinger написал(а):

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

Regards

WE

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07-05-2016
02:46 PM

07-05-2016
02:46 PM

Re: Seven math curves

Nice find!

I vaguely remember having heard (a long time ago) from a Tschirnhaus-curve (but not sure - I may mix up things and be wrong about this).

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07-05-2016
02:45 PM

07-05-2016
02:45 PM

Re: Seven math curves

Werner Exinger написал(а):

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

Regards

WE

We have 7 operators in Mathcad

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07-03-2016
12:02 AM

07-03-2016
12:02 AM

Re: Seven math curves

1. black+blue

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07-03-2016
12:04 AM

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07-03-2016
12:33 AM

07-03-2016
12:33 AM

Re: Seven math curves

3. black * blue = const (ovals Cassin)

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07-03-2016
07:13 AM

07-03-2016
07:13 AM

Re: Seven math curves

Nice worksheets.

I see that you, too, determine the limits of the radius L by hand (trial and error, I guess).

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07-03-2016
08:48 AM

07-03-2016
08:48 AM

Re: Seven math curves

4. black / blue = const (Apolinarian circle)

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07-03-2016
09:37 AM

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07-03-2016
09:41 AM

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07-03-2016
09:44 AM

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07-05-2016
12:47 AM

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09-11-2016
04:17 AM

09-11-2016
04:17 AM

Re: Seven math curves

7. blue-root of black - with new focuses and with two branches

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07-05-2016
12:45 AM

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09-10-2016
01:24 PM

09-10-2016
01:24 PM

Re: Seven math curves

With two branches: one log(Black, Blue) and others log(Blue, Black):

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07-03-2016
09:41 AM

07-03-2016
09:41 AM

Re: Seven math curves

> 5. black^blue=const

Nice, but the unit "m^m" is still wrong 😉

What about the "???"

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07-03-2016
09:59 AM

07-03-2016
09:59 AM

Re: Seven math curves

Werner Exinger написал(а):

> 5. black^blue=const

Nice, but the unit "m^m" is still wrong 😉

What about the "???"

Why wrong?

I'm going to do at my dacha for a bed of flowers in the form of this oval with a physical characteristic constant 7 (m^m), not 6 (ft^m) or 5 (m^ft)!

> ??? - I do not know what is this little close curve

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07-03-2016
10:15 AM

07-03-2016
10:15 AM

Re: Seven math curves

> Why wrong?

We had that discussion already in the other thread, so I won't repeat it here. Just one thought: (2m)^(3m) = 2^(3m) * m^(3m) = 8^m * (m^3)^m. So its NOT 8 m^m . Now do the same game with different numbers!

> I'm going to do at my dacha for a bed of flowers in the form of this oval

Why not, if a simple ellipse is not challenging enough 😉

> with a physical characteristic

Sorry, but its no physical characteristics and its a characteristic dealing with the numbers only, not the units. But it sure is a nice leisure activity anyway.

> > ??? - I do not know what is this little close curve

Obviously, if you did not make a mistake, its part of the solution curve. Just give it a try and see, if black^blue still is 4.

EDIT: There is a mistake: If L<1, then L2 would be negative and no solution exists!! But your "Coord" yields solution because L2 (as radius) is squared in the circle equation. You have to take care of this and simply let L run from1 upwards (L=1 would provoke a divison by zero, of course which could be dealt with an on error statement).

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07-04-2016
01:19 AM

07-04-2016
01:19 AM

Re: Seven math curves

Werner Exinger написал(а):

> Why wrong?

We had that discussion already in the other thread, so I won't repeat it here. Just one thought: (2m)^(3m) = 2^(3m) * m^(3m) = 8^m * (m^3)^m. So its NOT 8 m^m . Now do the same game with different numbers!

> I'm going to do at my dacha for a bed of flowers in the form of this oval

Why not, if a simple ellipse is not challenging enough 😉

> with a physical characteristic

Sorry, but its no physical characteristics and its a characteristic dealing with the numbers only, not the units. But it sure is a nice leisure activity anyway.

My friend in USA would like to create same bed of flowers (клумб с цветами) in his garten. He has a rule not with meter and cm but with feet and inch. I send to him the coordinate of 2 points (focuses) with feet and inch and the constant a with.... What numeric value and UNIT must I send in America? Or I must send the rule with meter and cm scale?

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07-04-2016
06:38 AM

07-04-2016
06:38 AM

Re: Seven math curves

Better send him the ruler in metric units as your flowerbed does not scale (the property a^b=const. does not scale). And don't forget to tell him that he should only use the numbers taken w/o units when he calculates the powers 😉

You haven't answered (2m)^(3m)=? and now (6,562 ft)^( 9,843 ft)=?

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07-04-2016
06:58 AM

07-04-2016
06:58 AM

Re: Seven math curves

Here are some curves which should scale. Simply stay with basic commutative operations + and * and simply use more points:

Here the points whose sum of distance from five points is constant:

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07-04-2016
03:00 PM

07-04-2016
03:00 PM

Re: Seven math curves

Werner Exinger написал(а):

Here are some curves which should scale. Simply stay with basic commutative operations + and * and simply use more points:

Here the points whose sum of distance from five points is constant:

Animation:

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07-04-2016
07:01 AM

07-04-2016
07:01 AM

Re: Seven math curves

And here is the same with constant product of distances

Guess I have finished playing around with those curves. Can't think of a way to derive a closed parametric equation for those beasts.

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07-04-2016
11:26 AM

07-04-2016
11:26 AM

Re: Seven math curves

Please do one more with 7 points - 7 is one fine number!

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07-04-2016
01:59 PM

07-04-2016
01:59 PM

Re: Seven math curves

Werner Exinger написал(а):

And here is the same with constant product of distances

Animation

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07-05-2016
08:58 AM

07-05-2016
08:58 AM

Re: Seven math curves

Werner Exinger написал(а):

And here is the same with constant product of distances

Guess I have finished playing around with those curves. Can't think of a way to derive a closed parametric equation for those beasts.

It is a lemniscate with 5 focuses - see please Лемниската — Википедия

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07-05-2016
02:54 PM

07-05-2016
02:54 PM

Re: Seven math curves

The discription is not available in the English or German version of Wikipedia.

I am not sure if all those curves should be called lemniscates.

In the two focal point case we speak of Cassini ovals and only if the constant product is the square of half of the distance of the two focals, we speak of a (Bernoulli) lemniscate. So the two focal lemniscate is just a special case of the Cassini curves.

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07-05-2016
12:39 AM

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07-05-2016
09:59 AM

07-05-2016
09:59 AM

Re: Seven math curves

Video Link : 7034 4. black / blue = const (Apolinarian circle)

Animation

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09-10-2016
01:04 PM

09-10-2016
01:04 PM

Re: Seven math curves

Bicycle Apollinaire - two branches: Black/Blue and Blue/Black: