Linked Questions

0
votes
3answers
2k views

Approximating the integral $\int_0^{0.1} \sqrt{1-1/2\sin^2(t)} dt$

How would I go about evaluating $I = \int_0^{0.1} \sqrt{1-1/2\sin^2(t)} dt$ to four decimal accuracy?
12
votes
2answers
8k views

Determining the angle degree of an arc in ellipse?

Is it possible to determine the angle in degree of an arc in ellipse by knowing the arc length, ellipse semi-major and semi-minor axis ? If I have an arc length at the first quarter of an ellipse and ...
1
vote
2answers
73 views

Having 2 independent segments made by 4 cartesian points, calculating x points of a smooth curve connecting the two segments

Drawing with an example of what Im trying to do I'm trying to make a sort of turtle program as a toy programming project. I can send instruction to go from A to B straight giving direction and ...
6
votes
1answer
256 views

Construction of new ellipse

Using a pencil, the thread was pulled on the ellipse. Then the pencil started to rotate around the ellipse. How to prove that the new geometric figure which the pencil drew is also an ellipse (with ...
2
votes
1answer
704 views

Generate random points on perimeter of ellipse

Sampling only from the uniform distribution $U(0,1)$, I am hoping to use transformations to create random values distributed uniformly around the perimeter of an ellipse. Eventually, I'd like to do ...
2
votes
1answer
583 views

ellipse uniform perimeter travel?

I'm trying to come up with a way that as I progress linearly from $0$ to $360$ degrees or $0$ to $2\pi$ radians I have the the corresponding position (P) on the perimeter of an ellipse to also travel ...
1
vote
1answer
240 views

Arc length of ellipse in different quadrants

This question is basically a follow-up or generalization of How to determine the arc length of ellipse? Given an ellipse with axes a and b, and the start and end angles $\theta_{start}$ and $\theta_{...
1
vote
1answer
54 views

can we say $x=aV\sqrt{a}$ in Kepler's third law? What else can we say?

we know that Kepler's third law says that the Period of the planet (time elapsed for a planet to perform a complete rotation around its sun) to the power of 3 is proportional to the orbit's semi-major ...
1
vote
1answer
152 views

Question about specific arclength over an ellipse problem

to see an image of what I'm talking about click this link: https://i.gyazo.com/909ccf0113fd26d21797f411a756ba1e.png In this image, arclength A is what we desire to be calculated. Point P is given and ...
0
votes
1answer
60 views

Find the length of $\{z \in \mathbb C: |z-1|+|z+1|=4\}$

Find the length of $\{z \in \mathbb C: |z-1|+|z+1|=4\}$. If we could write $z=x+iy$, then this is an ellipse of the form $$\frac{x^2}{4}+\frac{y^2}{3}=1$$ So $x=2\cos t, y=\sqrt{3}\sin t$, so the ...
-1
votes
1answer
292 views

How to calculate the distance travelled by a car in an elliptical track after a certain time given its angular speed

I have a car traveling on an elliptical race track at a constant angular velocity of A radians/sec. The angular velocity is calculated at the intersection of semi-major & semi-minor axis. I know ...
1
vote
0answers
50 views

How do I work out the distance of Venus orbit mathematically? [duplicate]

How do I work out the distance Venus travels in one orbit mathematically? I know the parametric equations for its ellipse but I need to work out the total distance travelled in its orbital period.
1
vote
0answers
66 views

Integration by substitution to find the arc length of an ellipse in polar form.

I have that $l/r = 1+e.\cos(x)$, for $l = a(1-e^2)$ (constant). The question asks for the mean distance over angle of the planet from the sun, where the planet moves on an elliptical orbit with the ...
0
votes
0answers
45 views

Angular gradient of an ellipse

This is my first post, I am not advanced in math so please be patient with me, I hope I can explain myself :) I am using a software called Substance Designer. It has a tool called pixel processor ...
0
votes
0answers
468 views

Ellipse circumference and 1/2 arc of first quadrant

For an ellipse (centered at 0,0), let a = 5.088 and b = 3.006. I used an equation to determine the circumference of ellipse. The approximation = 25.850. Now, I assume it is safe to say that each ...

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