Tagged Questions

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43 views

Express the length of the as a function of x

I am having problems understanding how to extract this information into a formula. ...
64 views

Is there a Taylor series for vector cross product?

I have this equation, where $u,v,w,a,b,Ɵ$ are constants. The RHS comes from the Geometric definition of the LHS $(u,v,w)(a,b,c)=||(u,v,w)||||(a,b,c)||\cos(\theta)$ Expanding the 2-norms ...
66 views

Bearings Problem

I'm presented with the following bearings problem. I believe I have graphed it correctly, although I don't know where to go from here. A US Coast Guard patrol boat leaves Port Cleaveland and ...
54 views

How long is the diagonal of this trapezoid?

Given a trapezoid $abcd$, with $|ab| = 1$, and angles $\angle dab = 3\theta/4$, $\angle abc = (\pi + \theta)/2$, $\angle bcd = (\pi - \theta)/2$, and $\angle cda = \pi - 3\theta/4$ (see figure below), ...
103 views

Are Euclidean distances a monotone function of inner products?

Does the sum of all pairs of inner-products of k vectors (real) have to decrease if the sums of Euclidean distances between all pairs of $k$ vectors happens to decrease? Similarly-if decrease is ...
133 views

Pseudo-pythagorean theorem

Pythagoras' theorem is a special case of the Cosine theorem for a angle of $90°$. But also for an angle of 60° and 120°, "aesthetical" special cases derive: $c^2=a^2+b^2\pm ab$ First question: Are ...
131 views

3D Game: Pitch Yaw Roll of a point

I have a flat elliptical plane and I'm trying to figure out how to represent it based on its direction. So I basically need to calculate its pitch, yaw, and roll. I have a camera at $C$, and a point ...
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How do I proof that $\angle ABP =\angle AP'B$ and that $P$, $Q$, $Q'$ and $P'$ are on 1 circle?

Given is a circle with center $M$ and a diameter $AB$. $k$ is the tangent to the circle at point $B$. On the circle there are two points called $P$ and $Q$, such that $P$ and $Q$ are both on the same ...
357 views

Formula to find the third point of triangle when two points and all sides are known?

I am writing a program in java. I looking for formula to determine the 3rd point in a triangle if the length of all sides and the coordinates of two points are known.
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Unit circle - how to prevent backward rotation

Let's assume we have a unit circle (0, 2$\pi$). Basically I have a point on this circle who is supposed to move only forward. This point is controlled by the user mouse and constantly calculate 25 ...
194 views

Internal polygon formed by drawing diagonals in a regular polygon

In an n-sided (n>4) regular polygon, label the vertices {0, 1, ..., n-1}. For each vertex i, draw a pair of diagonals: from i to (i+2) mod n and from i to (i-2) ...
45 views

Simpler solution to a geometry problem

In a set of geometry problems, I got this one: If in a triangle $ABC$ with segments $AB=8$, $BC=4$, and $3A+2B=180^{\circ}$, calculate the side $AC$ My solution was Let ...
103 views

Bound on the angle between a vector and a subspace

Suppose you have three complex vectors $x_1$, $x_2$, and $x_3$. Define $a = \angle(x_1,x_2)$, $b = \angle(x_1,x_3)$. My question is about $c = \angle(x_1, span(x_2,x_3))$, the angle between the vector ...
145 views

Trigonometry and algebra question

Given: The total length of ad + dc The lengths of each ab, bc and ...
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Trigonometry and algebra question [duplicate]

Given: The total length of ad + dc The lengths of each ab, bc and ...
306 views

Finding the x-coordinate of the max point of $y = x\sqrt {\sin x}$ so that it satisfies the equation $2\tan x + x = 0$

The maximum point on the curve with equation $y = x\sqrt {\sin x}$, $0 < x < \pi$, is the point A, Show that the x-coordinate of point A satisfies the equation $2\tan x + x = 0$ I ...
80 views

Optimal rotation to align a circle with external points

I have a circle $C$ with radius $r$ and a set of finite points $P=\left \{ p_1,p_2,\ldots,p_n \right \}$ are identified external to the circle $C$. These points may lie on the exterior or the interior ...
102 views

Find eigenspaces using ruler and compasses

I think this is an interesting question: In the 2-dimensional real vector space, we are given a linear transformation $f$. Suppose we already know the images of the standard bases, say ...
209 views

A question on Trigonometry (bisector)

If two bisector of a triangular is equal, then it is Isosceles triangular.
337 views

How to get coordinates of point knowing distance from x,y and angle?

I have such a problem : I am given : x,y $\|a\|$ $\alpha$ $\vec{v}$ and $\|v\|$ I need to get the coordinates of point X1Y2.
170 views

Draw a square around a point.

I have a point on the graph at position X,Y , and I have to draw a square around that point of side X m. I have described my problem in the image. I have taken an example square of 3 m. The ...
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Minimial parameters to discribe a point on the surface of a high dimensional unit sphere

Consider a 2N dimensional space, $x\in \mathbb{R}^{2N}$ is a point with constraint $||x||_2=1$ Thus $x$ is actually lies on the surface of a unit sphere. Given that we know the fact $x$ is always on ...
119 views

area of a circle - 3/4th

How to find the pixels of that line which is crossing the circle? Is there any formula? Iam getting the line's end points
197 views

Calculate coordinates of the a point in space with hypotenuse and two angles given

I have a cylinder with a length of $2$, and two angles for rotation around two of the axes. Functions for that are named $\text{RotX}$ (rotation around X axis) and $\text{RotZ}$ (rotation around Z ...
122 views

there are two docks

There are two docks, dock A and Dock B, on a large lake. The distance between the two docks is 72.5 km. Dock B is directly east of dock A. One day, a steam boat leaves from dock A at noon, and heads ...
604 views

Why do we use the Euclidean metric on $\mathbb{R}^2$?

On the train home, I thought I would try to prove $\pi$ is irrational. I needed a definition, so I used: $\pi$ is the area of the unit circle. But what is a circle? A circle is the set of tuples ...
574 views

How to plot N points on the surface of a D-dimensional sphere roughly equidistant apart?

Let's say I have a D-dimensional sphere with a radius R. I want to plot N number of points evenly distributed (equidistant apart from each other) on the surface of the sphere. It doesn't matter where ...
175 views

Length bisection from circular arc

I am not sure if the following result is well known. I stumbled across it from the paper The Perimetric Bisection of Triangles by Dov Avishalom, where the result was stated without proof. I am ...
187 views

Refraction equation, quartic equation

Given two points $P$ and $Q$, a line ($A$, $B$ - orthogonal projection of $P$, $Q$ onto the line) and a coefficient $n$, I want to find out such point $C$ that $\frac{\sin{a}}{\sin{b}}=n$ (in fact, ...
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Finding unknown 3D vector given 2 known vectors and 2 known angles

So I have a 3D vector math problem that I'm having difficulty solving. Basically I have two known vectors in the form (x,y,z), let's call them C and P, and I want to find a third unknown vector, let's ...
62k views

Solving Triangles (finding missing sides/angles given 3 sides/angles)

What is a general procedure for "solving" a triangle—that is, for finding the unknown side lengths and angle measures given three side lengths and/or angle measures?
845 views

Finding angles in a parallelogram without trigonometry

I'm wondering whether it's possible to solve for $x^{\circ}$ in terms of $a^{\circ}$ and $b^{\circ}$ given that $ABCD$ is a parallelogram. In particular, I'm wondering if it's possible to solve it ...
257 views

Algebra in trigonometry, algebraic proof?

The picture says it all. "Vis at" means "show that". My first thought was that h is 2x, which is not correct. Maybe the formulas for area size is useful? EDIT: (To make the question less dependent ...
2k views

Find the perimeter of any triangle given the three altitude lengths

The altitude lengths are 12, 15 and 20. I would like a process rather than just a single solution.