2
votes
2answers
70 views

Curve parametrization

When plotting following implicit function $x^4 + y^4 = 2xy$, what is the best way to parametrize it? I tried $y=xt$, but then I get $x=\sqrt{2t\over {1+t^4}}$ and $y=\sqrt{2t^3\over {1+t^4}}$, which ...
1
vote
1answer
44 views

Equation for this graph

I am trying to find an equation for the graph that crosses the Y axis at (0,100), X axis at (100, 0), is a curve with adjustable degree of "bending" and has an axis of symmetry y(x) = x. Here are few ...
2
votes
0answers
58 views

Should a “good” equation divide the plane?

At the question Is there any equation for triangle? (MSE) the answer given by Henning Makholm received the most upvotes. Therefore let's define the following triangle function $H$ with (a,b,c) the ...
2
votes
2answers
124 views

Curves with “constant speed”?

I am new to the concept of curves. Let us a assume we have a simple function such as $f:\mathbb{R}^+\rightarrow \mathbb R^+\quad f(x) := \sqrt{x}$. (Or $f(x)=\exp(x)$ or a polynomial etc.). We can ...
2
votes
1answer
40 views

Define together with the $x$-axis an area.

The curves $y = \sqrt{2x+3}$ and $y = x$ define together with the $x$-axis an area. Determine the exact value of the specific area. How do you solve?
0
votes
2answers
77 views

Graph of a curve

Today in my test, there was a question which had contour C: $|z+\dfrac{1}{z}| = 2$. What does the curve represent? Is it a discrete set of points or really a curve?
3
votes
1answer
499 views

Using equations to draw out complex objects

How do people come up with equations of curves to draw out complex objects? Some popular examples would include: batman curve & PSY curve. This stackexchange link explains the rationale for the ...
0
votes
1answer
92 views

Defining the movement of an object on a 2-dimensional plane

I am trying to define the movement of an object for a danmaku game I am making. Here is a link to some example gameplay (not my game, but a popular series in this genre made by Zun). Basically, I was ...
3
votes
2answers
136 views

How to mathematically color the regions bounded by a parametric curve?

Usually, if an implicit equation F(x,y) = 0 defines a curve (or curves) on the x-y plane, then we can use the inequalities F(x,y) < 0 or F(x,y) > 0 to color the regions bounded by the curve (or ...
1
vote
1answer
219 views

polar graphs and investigation

I am new to polar graphs and I am trying to investigate some certain cases: What happens when you change the $b$ value to different positive integers in polar equations of the forms: ...
3
votes
1answer
749 views

Can you write a non-piecewise equation that describes an arbitrary shape?

This batman equation thing got me thinking: for an arbitrary curve drawn on the Cartesian plane, can you write a corresponding equation which is not piecewise? What about closed shapes, a la the ...
319
votes
10answers
345k views

Is this Batman equation for real?

HardOCP has an image with an equation which apparently draws the Batman logo. Is this for real?