1
vote
1answer
35 views

Keeping the arc length constant between points in a spiral

I'm making a visualization of points in a logarithmic spiral and want to keep the arc length between points (image particles) constant. I read that in an Archemedian spiral arc length is ...
0
votes
1answer
22 views

Logarithmic spiral appears inverted

I'm learning to code the equation for a logarithmic spiral for a graphics visualization. However, it appears to be inverted with the radius getting smaller (rather than larger) toward the outside of ...
1
vote
2answers
28 views

Is equation for ellipse in polar coordinates correct?

Wikipedia gives the following equation for the conic sections in the polar coordinate system: $r = \frac{l}{1+e\cos\varphi}$. According to the article on conic sections, in case of an ellipse $e = ...
0
votes
1answer
27 views

Find points near end point of a line

Any equation to find points near to both start and end points of lines with different slopes. See image. Need P and Q. If Endpoints are named A and B, AP and BQ should be 1 cm
0
votes
2answers
32 views

Cartesian coordinates of lemniscate

A problem from Spivak's Calculus: Sketch the graph of the lemniscate $$r^2 = 2a^2\cos 2 \theta.$$ Find an equation for its cartesian coordinates. Show that it is the collection of ...
0
votes
1answer
30 views

Calculate if a Circle intersects a Arc

Have a Cartesian Plane cartesian plane And a Arc with the measures: point = 200, 200 radius = 50 start angle = 0 end angle = 180 And a Circle with the ...
2
votes
1answer
34 views

Representation of cardiod in the complex plane

I noticed that the complex function $$f(z) = \frac{2}{(z+i)^2}$$ seems to map the real line onto the cardioid given by the polar equation: $$r = 1- \cos(\theta).$$ I was wondering if there is a simple ...
0
votes
1answer
26 views

Polar equation for a Heptagon

What is polar equation for a Heptagon ? I need to move some Android views in the form of a heptagon, for i need to have polar equations for Heptagon like for x= rSine(Theta) and y=rcos(theta). is it ...
0
votes
1answer
20 views

Find a vector in cartesian coordinates given its relative location to another vector in spherical coordinates

Here is my problem: -I have an arbitrary normalized vector N in cartesian coordinates -I am trying to find normalized vector M, also in cartesian coordinates -I am given the azimuth and polar ...
2
votes
0answers
74 views

Shifting a plot in polar coordinates

Say we have the plot of a function $r=f(\theta)$ and want to "relocate" it to $(h,k)$. Is there a general procedure for this? I have tried the following tactic to no avail on the following example: ...
0
votes
1answer
71 views

Problem plotting hypotrochoids using a computer

I have been trying to use a computer to plot some hypotrochoids, but I've run into some issues. For those that are unfamiliar, the parametric equations of a hypotrochoid are: $$x(\theta) = (R - ...
0
votes
2answers
84 views

Plotting polar equations of circles not centered at (0, 0)

Good afternoon guys! I'm fairly new to polar coordinates and polar equations, so bear with me please. I understand the equation of a circle with radius $a$ centered at the polar coordinate $(r_0, ...
1
vote
0answers
46 views

Algorithm for finding nearest distance from a point to a curved surface in space

I need to write an algorithm which can find the nearest distance from a point in space to a 3D curved surface which is straight in vertical direction but its projection is an arc of a circle (Similar ...
2
votes
4answers
194 views

Linear combinations of sine and cosine

If you take a linear combination of the cosine and sine function, then the result is again a sinusoid, but with a new amplitude and phase shift. $$a \cos(\theta) + b \sin(\theta) = A \cos(\theta + ...
1
vote
2answers
118 views

Mathematical roses with $4n+2$ petals

In polar coordinates $(r, \theta)$, the equation $$r = \sin\left(a \theta\right)$$ gives a rose with $a$ petals if $a$ is odd, or $2a$ petals if $a$ is even. Thus, the number of petals generated for ...
1
vote
1answer
69 views

translate coordinates on circle to percentage?

I'm coming more from a programming point of view but the question is pure math. The only strange thing, I guess, is that the coordinate system is like this: ...
0
votes
0answers
20 views

Getting latitude/longitude from a 2d co-ord system [duplicate]

Given a latitude/longitude and a distance and bearing in relation to that point, how can I find the latitude/longitude of the new position? Distances can range from 0-100km so curvature of the earth ...
0
votes
1answer
360 views

Hyperbola in polar coordinates, what's wrong?

I read that the equation of a conic in polar coordinates is $$r=\frac{l}{1+e\cos \theta}.$$ But when I try to reduce the hyperbola $$x^2 - y^2 =1$$ to that form by setting $x=r\cos \theta $, $y=r ...
0
votes
1answer
45 views

Geometry finding area problem

A regular 2N -sided polygon of perimeter L has its vertices lying on a circle. Find the radius of the circle and the area of the polygon.
0
votes
1answer
159 views

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 ...
2
votes
1answer
45 views

What's the name of each pseudo-rectangle in a spherical surface?

Consider the common surface of a spherical segment crossed with a spherical wedge. This produces a pseudo-rectangle in the sphere surface, and a perfect rectangle in a mercator projection. What's the ...
1
vote
1answer
176 views

Moment of inertia of a circle

A wire has the shape of the circle $x^2+y^2=a^2$. Determine the moment of inertia about a diameter if the density at $(x,y)$ is $|x|+|y|$ Thank you
1
vote
1answer
146 views

What happens to a line in polar coordinates when orgin is moved and rotated in cartesian coordinates?

Let's say we have an Archimedean spiral in Cartesian coordinates. This corresponds to a line in polar system (i.e. $r=a\theta+b$). Now if I move the origin of the Cartesian coordinates system to ...
1
vote
2answers
122 views

Coordinate system conversion: what it is called what I'm doing?

I want to do a simple coordinate transformation and would like to know what is the rigorous way to describe this mathematically in order to be able to search for algorithms for more complex ...
1
vote
1answer
75 views

Polar coordinates parameters

Sketch in the same diagram the curves with polar equations $r=2a\cos\theta$ and $2r(1+\cos\theta)=3a$ and find the polar coordinates of their points of intersection. What is the polar equation of ...
2
votes
0answers
646 views

Parametrization of square to calculate Dot-product in line-integrals and area-integrals, electric field from $\frac{dB}{dt}$?

I am calculating 3A of Tfy-0.1064 in Aalto University. I realized here that I am misunderstanding something in vector calculus: the thing market in green particularly. I know $$\nabla\times E= ...
0
votes
1answer
191 views

Collision detection of two circular sectors in mixed polar and Cartesian coordinate

I am trying to solve the following collision detection problem. Suppose we have two circular sectors, each described in their own polar coordinate system with four values $r_1$, $r_2$, $d_1$ and ...
1
vote
1answer
160 views

Analytically derive n-spherical coordinates conversions from cartesian coordinates

I'm finding it difficult to find any non-geometrical derivation of coordinate conversions from cartisan to spherical. I can understand the derivations geometrically, because I can visualize the ...
1
vote
1answer
219 views

map on a unit sphere with polar coordinates

My brother, who is in hospital atm and cannot verify by himself asked me to post the following question, thank you in advance, and sorry if the topic has already been covered, i do not have the math ...
1
vote
1answer
705 views

How to convert the equation of a line from polar to standard form?

How do you convert a polar line to a line in standard form? That being, change a line with parameters rho and theta in a polar ...
1
vote
0answers
65 views

Knowing coordinates of a point having two coordinates and the distance.

I have the two geographic coordinates of the lower corners of a wall. So, for example, i want to know what is the coordinate that is for example 15cm on the right of the lower corner left. Is that ...
3
votes
1answer
787 views

Bézier approximation of archimedes spiral?

As part of an iOS app I’m making, I want to draw a decent approximation of an Archimedes spiral. The drawing library I’m using (CGPath in Quartz 2D, which is C-based) supports arcs as well as cubic ...
1
vote
1answer
125 views

Given an exact velocity and a “velocity range”, what is the relative velocity range?

I'm trying to calculate the relative velocity ($V_R$) between an exact velocity ($V_0$) and a velocity range ($V_1$). The exact velocity ($V_0$) is represented simply by ($course$, $speed$). The ...
0
votes
1answer
436 views

Orthonormal vectors in Polar coordinates, show $\hat{e}_R=\frac{(x,y,z)}{r}$

Definitions Unit vector has length 1. Orthonormal vectors are orthogonal and unit vectors. RobJohn's suggestions for the basis in polar coordinates, here, satisfy the criteria but how can ...
2
votes
0answers
914 views

Explain Triangle perimeter in polar coordinates

The question is to give a formula in $x$ and $y$ that gives all three sides of an equilateral triangle. The formula should not be true for points that are not part of the perimeter of the triangle. ...
0
votes
3answers
234 views

Visualizing why a right-angle rotation formula works in polar coordinates

I am trying to get a solid and intuitive handle on polar and spherical coordinates, and I'm getting stuck with what I think should be simple geometry: To find the unit vector in Cartesian coordinates ...
0
votes
1answer
623 views

definition of sinusoidal curve

I have question related with these two definition: In geometry, the sinusoidal spirals are a family of curves defined by the equation in polar coordinates $$r^n = a^n \cos(n \theta)$$ where $a$ is ...
1
vote
1answer
298 views

How to determine a shape is convex by giving polar form polynomial equation?

It is easy to determine concave, convex curve in xy coordinate. But I am placing a question that I only have a polar polynomial equation like r(ang) = a4*ang^4 + a3*ang^3 + .... + a0; How I can tell ...
5
votes
6answers
1k views

Why, conceptually, do limaçons $r=a+b\cos\theta$ have dimples when $|\frac{a}{b}|<2$?

Using calculus, I can justify that limaçons—the polar graphs of $r=a+b\cos\theta$ for various nonzero real values of $a$ and $b$—are dimpled when $|\frac{a}{b}|<2$, but that doesn't seem to yield ...