Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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## #1 Re: This is Cool » Cool art with geogebra! » 2012-05-02 12:45:13

Maybe I know how to make this. Can it graph inequalities in different color?

## #2 Re: Introductions » Imagine complex solutions to circle where both x and y can be complex? » 2012-05-02 12:28:27

Interesting idea!
Let's use a 4d space now: x,y,p,q
by (x pi) 05 (y qi) 05=1
we got x 05 y 05-p 05 q 05=1 and xp yq=0
{x 05 y 05-(1 x 05/y 05)p 05=1,q=xp/y}
We can't see it directly, so just plot z 05=x 05y 05 y 6­6-y 05/(x 05 y 05) and use your imagination!

## #3 Re: This is Cool » Find an equation showing special graph » 2012-05-02 12:06:05

benice wrote:
bobbym wrote:

The Batman equation?

Hi bobbym,

The original post is here.

Hi,benice;
I review the sites and infer that the earliest one is before 2011-07-29 09:35:26 (+8). But the site you gave just show "9 months ago", when the equation was flooding, so I don't know whether that is the original one.
We tried to plot it, only to found it abused "sqrt" so there is no plot. I tried to correct but gave up later because of the complex numbers (complex, not "i").

## #4 Re: This is Cool » How to draw the US Flag mathematically? » 2012-05-02 11:45:40

Thanks! That's really a superb job !

## #5 Re: Maths Is Fun - Suggestions and Comments » Implicit Equation Grapher » 2012-05-01 11:40:06

anonimnystefy wrote:

So that's why you did it. Either way,it is a very cool graph.

Try this: HTTP://www.xamuel.com/inverse-graphing-calculator.php?phrase=anonimnystefy&clientAction=15.click

## #6 Re: Maths Is Fun - Suggestions and Comments » Implicit Equation Grapher » 2012-05-01 11:27:01

bobbym wrote:

Hi Sumasoltin;

You left out the http:\\ so the img tags did not work.

Thank you for your care. Actualy, I did that on purpose. You know, there is a restriction for new menbers.

## #7 Re: This is Cool » How to draw the US Flag mathematically? » 2012-05-01 11:18:58

It couldn't be nicer for you to do that. But what you're considering is right so I hope that benice can put out them himself. Thank you all very much.

## #8 Re: This is Cool » How to draw the US Flag mathematically? » 2012-05-01 04:20:03

bobbym wrote:

Hi Sumasoltin;

I am definitely not in China. What is it you need?

Thank you very much. I just want to know how to "Drawing a US Flag using Inequalities" and draw "Monster Cow".

## #9 Re: Maths Is Fun - Suggestions and Comments » Implicit Equation Grapher » 2012-05-01 04:03:52

bobbym wrote:

Hi MathsisFun;

How about a color chooser for different colored graphs. Maybe the ability to graph 2 or more equations.

You could also add the best graph on this thread to the list of examples. So far, phrontister's dragonfly ( post # 33 ) get's my vote.

Aaa...Where's the dragonfly ?

## #10 Re: Maths Is Fun - Suggestions and Comments » Implicit Equation Grapher » 2012-05-01 03:48:16

MathsIsFun wrote:

I am so glad everyone likes it!

Some really wild equations, too

An example of where it goes wrong is bobby's "x^2*cos(x)=y*tan(y)" ... I don't believe the horizontal straight lines should be there at +/-π/2, they are an artifact of tan(y) changing sign, so the program assumes there is a zero in there.

The program has no way of knowing that the magical zero point is undefined. Any ideas on how to solve this?

A simpler example is "1/(1+x)=y"

Well, my stratege is finding out "/" to "remind" the program where it shouldn't show a blue point. Just plot a white line over it ! GrafEq has this trouble too and I use this way to hide the "patches". Another thing I want to say is that why not blod the plot so points-plot can be shown well?

## #11 Re: This is Cool » How to draw the US Flag mathematically? » 2012-04-30 15:49:53

Oh...still not work...Otherwise you're in China. The goverment do such things for no reason.
But I got this(may be rude but just a joke)

## #12 Re: This is Cool » How to draw the US Flag mathematically? » 2012-04-30 15:30:46

Sometimes China bloke some websites out, like google, youtube, so I think that's to blame.I can't visit benice's gallery.

## #13 Re: This is Cool » How to draw the US Flag mathematically? » 2012-04-30 14:28:26

May I ask for some help? What's the inequalities of the graphs? The website is blocked.

## #14 Re: Maths Is Fun - Suggestions and Comments » Implicit Equation Grapher » 2012-04-30 14:20:15

There are some amazing graph made by it.
In China, we use "NB" to show admiration and "great", so I found the "NB equation", NB equation, NB plot, and NB grapher.

## #15 Re: Maths Is Fun - Suggestions and Comments » Implicit Equation Grapher » 2012-04-30 14:05:43

Hi,MathsIsFun;
You've got a wonderful idea! But I have to say that someone did have the same idea and he made an wonderful grapher called GrafEq. But unfortunatly, the function of graphing has been out of time, so it's only for win6 or winXP.
He is Jeff Tupper, and he found the super inequality bellow. Why super? Its graph contains itself where 0<=x<=105 and n<=y<=n+16 ! n=96093937991895888497167296212785275471500433966012930665150551927170280239526642
46896428421743507181212671537827706233559932372808741443078913259639413377234878
57735749823926629715517173716995165232890538221612403238855866184013235585136048
82869333790249145422928866708109618449609170518345406782773155170540538162738096
76025656250169814820834187831638491155902256100036523513703438744618483787372381
98224849863465033159410054974700593138339226497249461751545728366702369745461014
655997933798537483143786841806593422227898388722980000748404719
As expected, this grapher has bugs, too.It allows x/0=0, x^(1/3)¡Ý0. It is the same problem of f(x,y)≈0 that you faced with.
Why not share your commands? Let's do this wonderful project together ! Many friends of mine and I want to improve it after our Chinese University Enterance Exam.
I've got a Jeff Tupper's paper about this, would you like to read ?

## #16 Re: This is Cool » Find an equation showing special graph » 2012-04-30 01:42:28

See it here:w w w.howtogeek.com/106221/stupid-geek-tricks-how-to-plot-the-batman-curve-in-google-search/
Well , math is a subject created by God, and you can make any thing into equations if you want. Pencils, flowers, waves, boats, mountains, bra and math(:P),and even a girl !

## #17 Re: This is Cool » Find an equation showing special graph » 2012-04-30 01:35:09

A leg of turkey exactly!

## #18 Re: This is Cool » Find an equation showing special graph » 2012-04-30 01:33:53

Aha! I learnt an American created the"Batman equation" in China.Did you hear about anything about it?

## #19 Re: This is Cool » Find an equation showing special graph » 2012-04-30 01:23:23

(x+13+sqrt((x+4)^2+4)-2sqrt((x+8)^2+4))^2*(12x*y^2+x^3-11y^2+x^2+7x-4)^3+(8y^2+6x^2-16x+4)^3*y^4*(x+13)^2=0 where x=-15 to 5, guess what's in it?
Tip:Thanksgiving Days

## #20 Re: This is Cool » Find an equation showing special graph » 2012-04-30 01:18:38

Oh, that's funny ! Without blanks "= (" was transformed into negetive face!
I did use k instead of 5,but a known number looks better.

## #21 Re: This is Cool » Find an equation showing special graph » 2012-04-30 01:13:01

ρ=1-cosθ , an old equation shows heart cruve (bottom instead I think).But I found "(x²+y²-1)³=x²y³" on WolframAlpha.
"Who found this?",I search it on Google and finally I learned it was Siehe Beutel.But how he found this?
We chosed Archimedes spiral: x²+y²=arc tan²(y/x)
we find that "tan x" is simillar to "x³",so we got
(x²+y²)³=(y/x)²
we find heart isn't a symmetrical shape,so we change "y²" by "y³"
As x becomes larger,the difference between "tan x" and "x³" becomes larger,so we plus "x⁴"
Aha~just a joke ! Maybe following can be turth.
He used a simple ellipse "x²+y²-xy=1".
We transform it to "x²+y²-1=|x|y".
NO ABS ! We get "(x²+y²-1)²=x²y²".
But now we lose the relation of that "x²+y²-1" is the same to "y" in "±" (I can't convey in proper way)
So we try the equation "(a²x²+b²y²-1)^(2k+m)=(by)^m*(abxy)^2k"
when a、b→1,there is the equation "
(x²+y²-1)^m=y^m"
So we have "|x|^m=((x²+y²-1)/y)^m=1"
Compare plots of "x²+y²-xy=1" and "x²+y²-y=1",we find only when x∈[-1/2,1/2] their difference become obvious,so m→0.
We make m=1，so k→+∞.
By trying,due to the equation's interval,when k=1 we get such a beautiful plot : (x²+y²-1)³=x²y³

## #22 Re: This is Cool » Find an equation showing special graph » 2012-04-30 00:23:56

WolframAlpha shows as this.

## #23 Re: This is Cool » Find an equation showing special graph » 2012-04-30 00:20:34

Oh,I got it ! Different softwares define "x^(2/3)" differently.It should be (x^2)^(1/3)

## #24 Re: This is Cool » Find an equation showing special graph » 2012-04-30 00:14:56

To bobbym;
Aaaa...what's wrong?

## #25 Re: This is Cool » Find an equation showing special graph » 2012-04-30 00:12:09

Hi anonimnystefy;
Aaaa......they are created in different ways.Some are using the transformation in which we replace x by x±f(x).