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Questions tagged [angle]

An object formed by two rays joining at a common point, or a measure of rotation. In the latter form, it is commonly in degrees or radians. Please do not use this tag just because an angle is involved in the question/attempt; use it for questions where the main concern is about angles. This tag can also be used alongside (geometry).

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Why don't circles have infinite degrees? [duplicate]

A triangle has 180 degrees. A square has 360. A pentagon has 540. A hexagon has 720. An octagon (which is starting to look a lot like a circle) has 1080. You see the trend?
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Another variant / corollary of Langleys adventitious angles triangle problem

I recently came across an elegant simple method on Youtube to solve the original Langley's problem using basic geometry principles. Worlds Hardest Easy Geometry problem I have also gone through ...
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1answer
33 views

Quaternion angle calculation

I'm working on a programming project, in this project I'm receiving an angle as a quaternion value, I partially understand how they work but I don't find any math to get the values I need. What I ...
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2answers
31 views

calculating new 3D position on sphere with angular velocity vector

I feel like this is actually pretty simple but still could not find any solutions so far... I'm trying to calculate the movement of a point in a rigid rod with the equation $ \dot P = [ v + \omega \...
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1answer
43 views

If $\cos( \alpha + \beta) = x$, then what is $\beta$? [on hold]

I have: $$\cos( \alpha + \beta) = x$$ What is the value of $\beta$?
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1answer
34 views

Find a point that is perpendicular to line and write it in javascript [closed]

Hi and sorry if my post is not the best but is my first time in something like this I have seen this post, I have two directional points. Point A going to point B. Each point has an X and Y ...
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2answers
44 views

Determine angles of a triangle given lengths of its sides

If I remember correctly this is high school material; I feel ashamed that I can't solve this now. Lengths of a triangle's sides determine its angles; but how to compute these angles?
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2answers
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Rotation of $e_1 \in \mathbb{R}^n$ in angles along the axis

I have the vector $e_1=(1,0,...,0)^T$ in $\mathbb{R}^n$. I would like to rotate it by angle $\theta_2$ along axis $x_2$, resulting in the vector $r_1 = (\cos(\theta_2),\sin(\theta_2),0,...,0)^T$. ...
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1answer
15 views

Angle between vector and x-axis in specific intervals

Given a vector going from a point $(x_0,y_0)$ to $(x_1,y_1)$ in a regular 2D-plane (i.e. an $\hat{x}$-axis pointing right and a $\hat{y}$-axis pointing up), I want to determine the angle between the ...
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14 views

Curvilinear abscissa = radius * angle - Circular motion

I would like to understand why: $$ s(t) = r \, \theta(t) $$ where $s$ is the curvilinear abscissa, $r$ the radius and $\theta$ the angle in circular motion. Thank you for your time.
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1answer
25 views

how to find slope of discrete point?

I am wondering if it is possible to find the slope at each point in the following dataset, ...
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0answers
20 views

How to know when a 360 rotation was performed around any given axis?

If I have any given axis, e.g. $\frac{1}{\sqrt{2}}\left[ \begin{array}{ccc} 0 & -1 & 1 \end{array} \right]$ and a rotational speed of $\omega = 1.5$ [deg/s] around that axis. How can I check ...
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0answers
21 views

Effect of angle error over distance (error propagation) [closed]

An angle of "$\theta$" has been measured with an error of "$s$" (in degrees). How the position error which is caused by this angle observation error at a distance of "$d$" (in meters) can be estimated?...
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2answers
51 views

Why is this angle not $22.5^\circ$? And does it have an exact value?

Since the angle which splits a square in a half, starting from it's bottom left corner, is $45^\circ$, I intuitively thought that, if I put two squares to be horizontally adjacent, the angle between ...
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1answer
59 views

Why is the sum of all external angles in a convex polygon $360^\circ$ and not $720^\circ$?

Why is the sum of all external angles in a convex polygon $360^\circ$? From my understanding, for each vertex in a convex polygon, there exist exactly $2$ exterior angles corresponding to it, which ...
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1answer
19 views

convex polygon considering three angles

If I choose three vertexes A,B,C in a convex polygon, it so happens that the sum of angleA,angleB,angleC appears to be 180 or larger. Why is this true? I tried drawing the polygon and making triangles,...
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1answer
32 views

Angles of convex polygons

For a convex polygon, show that the sum of any two interior angles is greater than the difference between any two interior angles. (the polygon has more than 3 sides) If I pick 4 dots A,B,C,D and say ...
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1answer
25 views

Defining angle in terms as a limit of ratios of volumes

Let $(\vec{w})^{\varepsilon}$ denote an open ball of radius $\varepsilon$ centered at $\vec{w}$ . The choice of open balls over closed balls is arbitrary. Let $S$ denote a set that's constrained to be ...
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2answers
101 views

geometry question in HK IMO prelim 2018

2018 IMO prelim in HK, Q.3: In triangle ABC, ∠ BAC = 18° and angle ∠BCA = 24°. D is a point on AC such that ∠BDC = 60°. If the bisector of ∠ADB meets AB at E, find ∠BEC. Any form of help will be ...
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1answer
17 views

calculate angle of line with negative slope

I want to use the formula $$ tan(\alpha)=m $$ for negative slopes but always get negative degrees. For instance, say the slope of a line $g$ is $-1$. Using the formula above (arctan$(-1)=\alpha$), I ...
3
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2answers
33 views

$AB_1$, $AB_2$, $AB_3$ are the altitude, angle bisector, median from vertex $A$ of $\triangle ABC$; arrange lengths $BB_i$ in ascending order

Consider an acute angled triangle $\triangle ABC$ such that $AB\lt AC$. If from $A$ altitude $AB_1$ is drawn, internal angle bisector $AB_2$ is drawn, and median $AB_3$ is drawn. ...
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0answers
14 views

Simply find point in circle border

This seems to silly for you expert guys in math but I am not good in this So Please help. Suppose you have clock of 330 * 330 pixels so I have radius 165 in circle. I want to find position of ...
5
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1answer
59 views

Calculate bevel edge Icosphere

I have an Icosphere with 80 faces, 120 edges. Now i am looking to find out what the angle is of the bevel between all the faces. With the bevel i mean the following see the image below: So i am ...
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1answer
21 views

Bidirectionally of the “Tangent Criterion”

I've recently been reviewing some basic geometry concepts when I saw this one in Evan Chen's fantastic "Euclidean Geometry in Mathematical Olympiads" (EGMO). Proving $(i)\Rightarrow (iii)$ is quite ...
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1answer
84 views

If I square a value units of radians, is the result in units of radians squared or is it still radians?

I am writing a paper on circular motion. A function given is $$T=Msω^2L$$ The units for $ω$ are $\text{rad}/s$. What are the units for $ω^2$? Are they $\text{rad}^2/s^2$ or $\text{rad}/s^2$? If they ...
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0answers
26 views

When the slope of the angle bisector is 1, is the product of the slopes of the 2 lines forming the angle equal to 1

When the slope of the angle bisector is 1, I have been told that the product of the slopes of the 2 lines forming the original angle is 1. Is this true?
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1answer
26 views

Finding the location of points of a triangle given the angle and length ratio.

Given that a point P is located at (-2.5,4.33) I need to locate the points A and B such that $\frac{PA}{PB} = \frac{4.77}{8}$ and $\angle APB = 55^o $. A and B must be on the -ve part of the x axis. ...
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1answer
26 views

Signed angle in plane

What is the formula to compute the signed angle between two vectors $u, v\in\mathbb{R}^2$ where positive angle is equivalent to a counter-clockwise rotation on the plane In other words I would like ...
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0answers
19 views

Orthogonal unit vector in spherical coordinates

A particle is traveling in the direction of the positive $z$ axis, until eventually, it is deflected. The new direction is given by an azimuthal angle (w.r.t. the positive $z$ axis) $\theta$ and a ...
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2answers
38 views

Fast way to compare angles w/o their measures

I need an efficient way to compare the measures of two angles in $\mathbb{R^2}$ that ideally relies on the smallest number of arithmetic operations and no trigonometric operations (no $\arccos$) or ...
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1answer
32 views

Finding sign of an angle without calculating the angle itself

Say we have an angle between vectors $P_1$ and $P_2$ in $\mathbb R^2$ whose vertex, $O$, is at the origin. I would like to know the sign of the smallest signed angle between $P_1$ and $P_2$ such that $...
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2answers
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Prepend a vector with 90 degree angle to an existing one

First of all: my knowledge in mathematics is a bit rusty, so no matter how simple my question is, I afraid I in every case need a somewhat detailed answer: I have a line from coordinates (x1,y1) to (...
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2answers
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Looking for correlation between length and angle

The problem I'm facing might be rather easy to solve, but I can't think of a way how to do it atm. I want to clip straight 90-degree and some other degree lines. If I clip them at a fixed height (like ...
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0answers
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Calculate 3d Rotation Maintaining Orientation

My Current Setup: Let's assume we have these 3 axes in 3d space. Let's also assume that x = blue; y = red; green = z; To calculate a rotation on the x axis, i.e.,...
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1answer
26 views

How to figure to the angle between a plane defined by three 3-dimentional points and a line defined by two

I'm writing a simple 3D render engine. In 3D graphics, everything is made of triangles. To figure how bright to make each triangle, it needs to know what angle it is relative to the direction of the ...
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2answers
34 views

Height of a Triangle, and a Progression of Triangles

I am researching some algorithms and it turns out that the following figure I made can model what is happening in a "step". I am not a mathematician, so I was having a hard time with this one. The ...
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3answers
52 views

Changing my Clock

I was given a problem in class. Let's say I bought a clock with no numbers on it (has only the hands). Because of the recent time change, I had to change my clock one hour back. In order to do this, I ...
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1answer
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Determine angle between 2 vectors.

If there are two vectors given $$\vec {OA} = \hat i + 2\hat j~~\text{and}~~\vec {OB} = 4\hat i + p\hat k $$ Then find the values of $p$ for which $\angle AOB = \cos^{-1}(\frac{1}{5})$. Would someone ...
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1answer
32 views

Should dot product must be applied on values of same scale

I have points in $n$-dimensions. I want to find the points which lie on one side of the plane and other lies on the second side and i'm trying to do this with the help of dot-product. Suppose i ...
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1answer
33 views

A rotation of 30 degree

What does it mean if an object moves 30 degree ? What will be its position now ? ( The concept of angles looks abstract to me. I cannot visualise it.) Thanks!
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0answers
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Concept of angle with circle

Has the concept of angle originated from circles ? I don't understand the concept of angles. I want to know how people start using the word "angle" in mathematics. When I want to know about angles, ...
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4answers
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$P$ is a point on the angular bisector of $\angle A$. Show that $\frac{1}{AB}+\frac{1}{AC}$ doesn't depend on the line through $P$

The point $P$ is on the angular bisector of a given angle $\angle A$. A line $L$ is drawn through $P$ which intersects with the legs of the angle in $B$ and $C$. Show that $$\dfrac{1}{AB} + \dfrac{1}{...
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0answers
37 views

Cardan (or Tait-Bryan) angles z-x-y and rotation matrix - Proof

I'm trying to get the following rotation matrix (cardan angle sequence z-x-y): To do that, I multiplied the three elementary rotation matrices $R_zR_xR_y$, but the result is different: Can you tell ...
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0answers
12 views

Move Point to corner of 3D Plane

I have one 3D plane which is act like a wall which always rotated Euler y angle. on that plane I have to add another Plane with 2 Position with the same angle wall has. I did this with ...
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1answer
41 views

How to compute angle of two points using tangent in a plan?

I have to realize a wrapper for $n$ points given by the user, where $2 \le n \le 10$. Therefore, I have to be able to know the order of covering all the points and generating the figure. So, I want ...
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2answers
26 views

What is the angle from (0,0) to (longitude, latitude)?

Starting on the crossing between the equator and the Greenwich meridian (0,0), one can proceed to any point on Earth with a given longitude and latitude along a great circle. Seen from the centre of ...
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1answer
36 views

Triangle with all reflex angles?

I was thinking about how a triangle could have all reflex angles. it would look like a regular triangle but the inside would be the outside and the outside would be the inside. Such a triangle would ...
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2answers
31 views

Find reflex angle with 3 points and their plane normal

I have 3 points in 3D and I want to calculate $ABC$ angle, which could be reflex angle. I also know the normal of the plane they are in. Is there a way to calculate the angle? EDIT: Take a look at ...
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0answers
31 views

Measuring Angles without Measure

Is there a (reasonable) way to measure angles without using measure? By measuring angles, I mean assigning something along the lines of degrees or radians to it. By measure, I mean measure in the ...
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1answer
29 views

Find the angles between two solids

I have 2 solids (A and B) and I need to find the three angles between their x, y, and z axes. If I calculate the geometrical center of the two solids (Ax, Ay, Az and Bx, By, Bz), is it correct to ...