# Tagged Questions

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### How would I normalize the slope of a line?

Assuming I have different lines with different slopes, I would like to compare the slope of each line as relative to one another. The program I am currently writing needs to compare the slopes of the ...
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### Area of a triangle - straight lines

Question: What is the area of the triangle formed by the line $x + y = 3$ and angle bisectors of the pair of straight lines $x^2 - y^2 + 2y = 1$. Well I really have no idea how to even start the ...
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### Circle - finding the equation

Question: Find the equation of a circle whose center is in the first quadrant; touches the x-axis at (4,0) and makes an intercept of length 6 units on the y-axis. I am getting a faint idea where to ...
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### How is equation art created [duplicate]

A friend of mine sent me a Wofram Alpha link to a parametric curve that creates a detailed drawing of a game character. The parametric equation that draws it is about ~9 screens tall on my ...
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### Find a projectivity to create a graph.

I have the tetrahedron {xyzt=0} in projective space with homogeneous coordinate (x,y,z,t). I need to create a graph but the tetrahedron in affine coordinate is {xyz=0} and I can't visualize the ...
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### How to normalize a slope?

Say I have two slopes and two averages for a sample: $m=4{,}000$ dollars/day, average $a=50{,}000$ $n=80{,}000$ dollars/day, average $b=700{,}000$ Graphically, $n$ is very ‘steep’ compared to $m$. ...
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### Graphing inequalities, elementary geometry (Highschool level)

I am going through some past papers, and one of the few questions I need help with are: For the second one, relating to plotting the square root of 4 - $x^2$, I did a table of values starting ...
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### Ordering angles using max and min functions

I'm using the awesome Desmos Graphing calculator to graph cyclic quadrilaterals. The idea is that the user can drag a slider to change the value of the angle of each point A, B, C and D. I have done ...
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### Can an equation represent a curve in 3D space?

I tried to get a equation that can represent a spiral like spring: $$z=\frac{height}{2\pi }\cdot \arctan \left ( \sqrt{\frac{radius^{2}-x^{2}}{radius^{2}-y^{2}}} \right )$$ I am not sure about the ...
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### Find the locus of points

Find the locus of points, the distance between them and the point $(2,1)$ is equal to the distance between them and the straight line $4x = 3y$ I know that it is the definition of a parabola But I ...
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### Question on Cobweb Diagram

Let f be a real map and assume that the points a and b form a limit cycle of order two of f. Derive a simple formula for the derivative of the second iterate of f at a.
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### Detect Regions Described By Lines in Rectangular Coordinates

Need some help from the superior math minds here. This problem is part of a software project. Essentially, I have a Cartesian grid. The user can create lines by plotting points (every 2 points ...
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### Very interesting graph!

I found a VERY interesting graph on http://www.xamuel.com/graphs-of-implicit-equations/. It looked very, very cool, but the equation of the graph is so simple! Here is the image of the graph: My ...
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### Plotting an ellipsoid

I need to draw an ellipsoid with an equation on this form: $$(Kx+y+z)x + (Ky+x+z)y + (Kz+x+y)z = 1$$ where K is a constant. Here is an example of wolfram drawing it for $K=8$: http://goo.gl/Ds5WWe ...
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### Plot the curve $y^2 = (x^2 +12x +36)/(x^4 -4x^3 - 12x^2 - 32x 64)$

Can you help me find the following to plot this curve, $$y^2 = \frac{x^2 +12x +36}{x^4 -4x^3 - 12x^2 - 32x 64}$$ In Explicit Form Find the Symmetry X & Y intercepts Vertical and Horizontal ...
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### find a common plane which contains two points (NP hard?)

In this problem the coordinates of 4 points are given. $p_{0}=(x_{0},y_{0},z_{0})$, $p_{1}=(x_{1},y_{1},z_{1})$, $p_{2}=(x_{2},y_{2},z_{2})$ and $p_{3}=(x_{3},y_{3},z_{3})$ I need to find the ...
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### Visual\Geometric characterization of associativity

Given a group $(G,f)$, I'm trying to characterize the graph of $f$ maybe in a more visual or geometric way. I'll explain a bit more: 1) because $f$ admits the zero element axiom of a group operation, ...
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### Formula for solving for Cx and Cy…

I'm trying to create a formula to find the third point in a triangle based on two known points and three known sides. Known Sides: $AB, BC, AC$ Known Points: $A(x, y), B(x, y)$ Unknown Points: ...
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### Determine third point of triangle when two points and all sides are known?

Determine third point of triangle (on a 2D plane) when two points and all sides are known? A = (0,0) B = (5,0) C = (?, ?) AB = 5 BC = 4 AC = 3 Can someone ...
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### how to scale a function?

My intuitive understanding of scaling a function $f(x)$, is that $$f'(sx) = f(x),$$ where $s$ is the scaling factor. For example, $f(x) = x^2$, and $s = 2$, then plot them out, the blue one is ...
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### Curve stitch primitive calculation

I want to calculate the intersection points of the following image: Assume that the three points of the triangle could be located anywhere. How would I do this?
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### Help me conclude a statement about two points given the following…

Two points on the graph of $y=kx^p$ are labeled $A$ and $C$. Point $A$ has coordinates $(a,b)$, where $0<a<1$ and point $C$ has coordinates $(c,d)$, where $1<c$. If we are told that that the ...
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### Defining a spiral in polar coordinates

I'm trying to find a general form for a spiral that fits the following criteria: the inner radius is $N$, and for any point $q$ on the spiral, the arc length from the start of the spiral to $q$ is ...
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### rotate graph of function by 180

suppose that we have graph of function $$f(x)=1+x\cos(x)$$ and we should rotate it by $180$ degree,question is what is a function which describe new graph?answer is $$f(x)=x\cos(x)-1$$but i can't ...
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### How can I draw a polygon from a set of angles?

In recreational mathematics, polytans are polygons formed by edge-connecting isosceles right triangles. Order-n polytans are those constructed from n such triangles. My question is this: Given a ...
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### Draw curves and planes in latex [closed]

I want to submit a paper and the only thing that's left to do is to add some graphics. My deadline is on Wednesday/Thursday. What I want to do is some basic curve/plane drawings. Here is an image: ...
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How do you read this graph: Function is: $f(x, z) = 1-e^{xz}$ How would I read the graph say $x = 3, z = 0.8$, which would make $y = 0.9092820647$ How do I find $y$ on the graph? Thanks.
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### 2D Eculidian matrix to 2D cartesian graph/plan

Can anyone help ? I am trying to convert a 2D matrix of distances to a 2D graph. For instance, I would like to go from this : ...
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### 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 ...
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### How can I determine the shape of a graph with $x^2$, $x$, and $y^2$ terms?

I'm working through a multivariable calculus course. I'm ~5 years removed from my most recent calculus course, and ~10 years removed from my most recent trigonometry course. While I'm understanding ...
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### understanding (and plotting) a surface (from implicit to parametric?) [duplicate]

Possible Duplicate: Automation of 3D Paper Modeling i am a programmer and not a mathematician, and my math knowledge are a little bit rusty. i have found this nice picture surfing on the ...
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### Calculating closest and furthest possible diagonal intersections.

Calculating closest and furthest possible diagonal intersections. Please refer to the image attached. It represents a $2D$ grid with the following properties: The grid origin is $(1,1)$ at the ...
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### Calculate closest point without calculating hypotenuse or linear length in 2D space.

Given n number of (x, y) points, I want to find out which is closest (linear distance) to the point of origin (1, 1). Both x and y will always be positive integers. ...
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### 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 ...
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### Using GeoGebra for Web based Graphical Problems [closed]

How can I make my documents available those I produced with GeoGebra on this site to share or ask for example? Which format I should choose to save or convert?
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### Position of 3 circles intersecting at the centre of bounding box

Here's what I feel is a neat challenge: I'm building a data visualization comprised of 3 circles of dynamic sizes. I want to have them all intersect at the centre of a bounding box that will also be ...
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### How to find the maximum & minimum possible Location within a graph?

For example, I have a graph having size of 480 width x 300 height. I am able to calculate the center point ( & that is 240,150 ). Now my question is as follows. I have a location/vertex on that ...
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### Calculate line graph x and y without knowing max/min of data set

This question pertains to programing but is really a math question. I am building an application that draws a line graph, similar to a stock line graph. The problem is I am not starting with a known ...
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### 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 ...
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### Is this Batman equation for real?

HardOCP has an image with an equation which apparently draws the Batman logo. Is this for real?
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### In the area of sphere, which angle with $0\leq \alpha<2\pi$ and which angle with $0\leq \beta < \pi$?

I am lacking the skill of visualizing the problem, picture here, to decide the right intervals. The way I do it currently is to try things but the technique fails with anything more complicated to 2D. ...
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### Converting parametric equation to Cartesian one

A curve has parametric equations $$\begin{array}{rcl} x & = & \cos(t)\\\ y & = & \frac{1}{2}\sin(2t) \end{array}\qquad \text{ for }0\leq t \leq 2\pi.$$ Show that the ...
I have a query below, and want to understand the reason of this in detail. Here is the graph of $x^2+(y-\sqrt{x^2})^2=1$ drawn by Wolfram Alpha: In this equation if you replace the term, ...
Assuming I have the graph of a function $f(x)$ is there function $f_1(f(x))$ that will give me a rotated version of the graph of that function? For example if I plot $\sin(x)$ I will get a sine wave ...