0
votes
2answers
44 views

Find the value of $a$.

please help I'm lost on what numbers to add or what formula to use
0
votes
2answers
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. ...
0
votes
2answers
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 ...
1
vote
3answers
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 ...
0
votes
1answer
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), ...
0
votes
1answer
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 ...
8
votes
5answers
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 ...
1
vote
0answers
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 ...
0
votes
1answer
32 views

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 ...
2
votes
2answers
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.
1
vote
1answer
52 views

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 ...
0
votes
1answer
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) ...
1
vote
1answer
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 ...
1
vote
0answers
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 ...
2
votes
1answer
145 views

Trigonometry and algebra question

Given: The total length of ad + dc The lengths of each ab, bc and ...
1
vote
0answers
28 views

Trigonometry and algebra question [duplicate]

Given: The total length of ad + dc The lengths of each ab, bc and ...
1
vote
1answer
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 ...
4
votes
1answer
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 ...
7
votes
2answers
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 ...
1
vote
2answers
209 views

A question on Trigonometry (bisector)

If two bisector of a triangular is equal, then it is Isosceles triangular.
1
vote
2answers
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.
0
votes
1answer
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 ...
0
votes
1answer
29 views

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 ...
1
vote
2answers
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
0
votes
0answers
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 ...
0
votes
1answer
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 ...
12
votes
4answers
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 ...
3
votes
1answer
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 ...
1
vote
1answer
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 ...
4
votes
2answers
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, ...
2
votes
1answer
41 views

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 ...
16
votes
1answer
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?
10
votes
4answers
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 ...
2
votes
3answers
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 ...
7
votes
3answers
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.
9
votes
2answers
504 views

geometric meaning of a trigonometric identity

It follows from the law of cosines that if $a,b,c$ are the lengths of the sides of a triangle with respective opposite angles $\alpha,\beta,\gamma$, then $$ a^2+b^2+c^2 = 2ab\cos\gamma + 2ac\cos\beta ...
3
votes
2answers
328 views

Calculate measurements for a diagonal fence beam

Given the width W and the height H of a rectangle, and the thickness T of a beam extending exactly from the upper left corner to the lower right corner as shown, how do I solve for length X and angle ...
3
votes
1answer
63 views

How do I find a point $(x_1,y_1)$ if I have an origin point $(x_0,y_0)$, a distance, and $\theta$?

I'm trying to figure this out for player movement in a video game but I'm having trouble figuring it out: How do I find a point $(x_1,y_1)$ if I have an origin point $(x_0,y_0)$, a distance, and ...
3
votes
2answers
396 views

Diffraction and Computer Generated Holography Calculations

I've tried this through Mathematica, and hit my own limit in math ability trying to do this, both to no avail. I'm assuming there is no way to do so, as a simple solution to this problem would be a ...
4
votes
1answer
242 views

Similar - perspective triangles implies corresponding sides are parallel?

In a general homothetic transformation, if two triangles have corresponding sides parallel then the lines joining respective vertices are concurrent at the homothetic center. I was wondering if the ...
2
votes
1answer
359 views

3d axis rotation

I have a vector V= and several line segments Seg1, Seg2, Seg3, Seg4. I want to know how to rotate each of the line segments so that the X axis is parallel to my given vector. How can I do this? ...
1
vote
0answers
216 views

Calculating the Epsilon Neighborhood of line segments in 3d

I am working on a trajectory clustering algorithm (in C++) and one of the steps required in this algorithm is to take a set of 3d line segments (D), and for each line segment (L) in D, to calculate an ...
1
vote
2answers
110 views

Radius of a hypercube at a given angle

For a ray from the origin with a given angle in $R^n$, I am trying to find the radius at which that ray intersects the frontier of the unit n-cube. In two dimensions, the picture is this: Given ...
2
votes
2answers
144 views

Find the Outgoing Edge with the Smallest Angles, Given one Incident Edges and Multiple Outgoing Edges

I have one incident edges and multiple outgoing Edges, for which I want to pick an outgoing edge such that the angles between the outgoing edge and the incoming edge is the smallest of all. We know ...
5
votes
3answers
990 views

How to determine arc measures from angles between secant and tangents (without trigonometry)

Given a circle, a point $H$ outside the circle, segments $\overline{HE}$ and $\overline{HT}$ tangent to the circle at $E$ and $T$, respectively, and points $I$ and $G$ on the circle such that $I$, ...
2
votes
5answers
257 views

What type of triangle satisfies: $\cot \biggl( \frac{A}{2} \biggr) = \frac{b+c}{a} $

If in a $\displaystyle\bigtriangleup$ ABC, $\displaystyle\cot \biggl( \frac{A}{2} \biggr) = \frac{b+c}{a} $, then $\displaystyle\bigtriangleup$ ABC is of which type ?
5
votes
3answers
3k views

Euler angles and gimbal lock

Can someone show mathematically how gimbal lock happens when doing matrix rotation with Euler angles for yaw, pitch, roll? I'm having a hard time understanding what is going on even after reading ...
20
votes
7answers
3k views

How to prove $\cos \frac{2\pi }{5}=\frac{-1+\sqrt{5}}{4}$?

I would like to find the apothem of a regular pentagon. It follows from $$\cos \dfrac{2\pi }{5}=\dfrac{-1+\sqrt{5}}{4}.$$ But how can this be proved (geometrically or trigonometrically)?
1
vote
2answers
653 views

Deriving volume of parallelepiped as a function of edge lengths and angles between the edges

In Wikipedia it is stated that the volume of the parallelepiped given its edge lengths $a,b,c$, and the internal angles between the edges $\alpha ,\beta ,\gamma $ is: $V=abc\sqrt{1+2\cos \alpha ...
4
votes
3answers
3k views

Find the coordinates in an isosceles triangle

Given: $A = (0,0)$ $B = (0,-10)$ $AB = AC$ Using the angle between $AB$ and $AC$, how are the coordinates at C calculated?