For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, angles.

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0answers
11 views

Fitting shapes of know sizes on another larger shape in diagonal fashion

How can I place shapes of known dimensions (with variation) on a larger shape, when intersection of these shapes is permitted and I must make the biggest gap between them? Please note that I wish to ...
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0answers
27 views

How show that the points S, U and A are collinear?

Circle $\omega$ is described on $ABC$. The tangents to the $\omega$ at points $B$ and $C$ intersect at $T$. Point $S$ lies on the line $BC$ and $AS \perp AT$. Points $B_1$ and $C_1$ are points of ...
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0answers
18 views

How to compute or describe the geometric distance between two 3*3 homography matrices?

The problem is similar to this, are there any geometric methods that can measure the distance between two homographies and tell whether these homographies can describe the same or similar ...
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2answers
46 views

Does Bertrand paradox depend solely on lines in estimating probabilities?

Why does Bertrand Paradox depend on lines in estimating probabilities of its different methods? For example, in method-1, the probability is calculated by comparing the arc of the circle that ...
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1answer
55 views

Cubohemioctahedron

Am I missing something here? Do I see shapes differently than everyone else? A Cubohemioctahedron is cited to have a Euler characteristic of negative 2. This is because most texts say its 10 faces ...
0
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1answer
105 views

number of ways to choose a convex subset that contains exactly 98 points (from MIT-Harvard Math Tournament) [closed]

A set of points is convex if the points are the vertices of a convex polygon (that is, a non-self intersecting polygon with all angles less than or equal to $180^\circ$ ). Let $S$ be the set of points ...
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2answers
32 views

Find a bisector point of a circle

The coordinates of $A=(x_{0},y_{0}$) and $B=(x_{1},y_{1}$) are given. How to find the coordinates of $C$ and $D$ as per given information below. ABC is equilateral triangle such that $AB=BC=CA$ ...
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1answer
48 views

How can you prove the triangle sum theorem?

Some things to consider: -This theorem has proved very, very many theorems many of which with trig, so you can't use any theorems that have been proven with the triangle sum theorem. -The Triangle ...
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3answers
48 views

Find $LK_1^2 + LK_2^2 + \dots + LK_{11}^2$. [closed]

$K_1 K_2 \dotsb K_{11}$ is a regular $11$-gon inscribed in a circle, which has a radius of $2$. Let $L$ be a point, where the distance from $L$ to the circle's center is $3$. Find $LK_1^2 + LK_2^2 + ...
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0answers
36 views

Proving that two or three segments are concurrent using complex numbers or vectors.

For example if we have a triangle and we want to prove that the medians all intersect at a point, using complex numbers (or vectors); how do we do that? (This is not my main question) My problem is ...
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1answer
27 views

Cones: Face of intersection is intersection of faces?

I'm writing on behalf of a group project where we are currently looking at basic geometry; in particular we are interested in polyhedral fans. We wish to prove that (abusing terminology somewhat) the ...
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0answers
10 views

lat/lon spherical coordinates to equidistant spherical coordinates

How to transform spherical data expressed in latitude/longitude pairs (parallels/meridians) in a new set of pair expressed just in parallels pairs? In other words, I need to transform data expressed ...
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2answers
43 views

How to rotate cuboid to plane

I have a cuboid with 8 points that is axis aligned with its center at the origin 0,0,0. Now I have a plane and want my cuboid to rotate so that instead of being axis aligned, it is now aligned to this ...
0
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1answer
53 views

Is there a way to visualize, like a picture in mind, the $n$-th derivative?

Is there a way to visualize (like a picture in mind) the $n$-th derivative ? For $n=1$ is the tangent line and we can visualize it quite well. More abstractly is it possible to see the geometric ...
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2answers
52 views

What is your favorite proof of the Pythagorean Theorem? Why? [duplicate]

My favorite is Euclid's original proof for two reasons: First, it requires minimal raw material. It only needs the result that the area of a triangle is half the area of a rectangle with the same ...
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4answers
109 views

Is it possible to put an equilateral triangle onto a square grid so that all the vertices are in corners?

In the following collection of problems - arXiv:1110.1556v2 [math.HO] - the following question is posed: Is it possible to put an equilateral triangle onto a square grid so that all the vertices ...
3
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1answer
48 views

The length of an quarter outer circle given an inner quarter circle of known length unknown radius.

This question was asked by someone on reddit. He wants to know the length, $K$, that a beam must be to surround a quarter circle segment of length $L$ at a distance $d$. This is his drawing. ...
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1answer
22 views

Volume of the cone in terms of sphere radius inside it

I need to find the volume of this cone. I know that there exists a ratio between the basis area and the transvelsar cut made into the sphere in the drawings, such that the ratio between the two áreas ...
1
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1answer
33 views

How to find the points of intersection of the perpendicular vector two skew lines

Correct me if im wrong, but this is what i know so far The cross product of two skew lines is the perpendicular vector between both those lines. The perpendicular vector intersecting two skew lines ...
0
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1answer
23 views

Visualization for “Cutting off a Corner of a 2-meter Square”

Corner of a 2 meter square is cut off to form a regular octagon. Determine the length of the resulting side of the octagon? Answer is 0.828 I need help visualizing this; if you cut off a corner of a ...
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0answers
27 views

The definition of face - in regard to polyhedral fans

Question: How is face defined rigorously for bullet point 2 below. Definition: A convex polyhedral fan, $F$, of polyhedral cones, all living in the same vector space, requires two things: If ...
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1answer
20 views

In an icosahedron subdivided n times, how can I find the coordinates of adjacent centroids?

I think it would be helpful to refer to this image when trying to follow my description: http://i.imgur.com/nRXQo3W.jpg (taken from http://experilous.com/1/blog/post/procedural-planet-generation). ...
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0answers
13 views

Rotating and reflecting ellipses in 2D

Let $f(x,y) = x^2 + \dfrac{r^2}{a^2}y^2 - r^2$ where $a$ and $r$ are real numbers. Let $E = \{(x,y)\in \mathbb{R}^2: f(x,y) = 0\}$. Note $E$ is an ellipse. Then, let $R_\theta$ denote a rotational ...
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1answer
37 views

Finding the Distance Between A Point in the Circumference and a Point in the Radius

Two people A and B started to walk from the same point on the circumference of a circle whose radius is 300m; each person walking at the rate of 120m/min. If A walks toward the center of the circle ...
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2answers
254 views

Can you define arc length using a piece of string?

In calculus, how we calculate the arc length of a curve is by approximating the curve with a series of line segments, and then we take the limit as the number of line segments goes to infinity. This ...
0
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1answer
11 views

Visualization of Rhombus made of Radii and Chords

A rhombus is formed by two radii and two chords of a circle of diameter 20 units. What is the area of the rhombus? Answer is 86.60 Ok I know i should provide a solution for this but my main problem ...
3
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0answers
471 views

Two circumcircles of triangles defined relative to a fixed acute triangle are tangent to each other (IMO 2015)

I'm posting here the question because I want to see a nice synthetic solution (not using complex numbers or inversive geometry) for the 3rd problem from IMO 2015. The problem is as follows: Let ...
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0answers
23 views

Statistics,standard deviation,spread,gemoetric meaning

What are the geometrical interpretations/meanings of these statistical quantities: mean, standard deviation and spread?
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1answer
29 views

Asymptote of sine function!

I am reading about asymptotes in my personal reading. I am thinking not all open curves will have asymptotes as I am not able to comprehend an asymptote for Sine Curve. Is it right/wrong?
2
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0answers
53 views

3D Shape with only coplanar faces?

I just thought of this problem, and it's bugging me that I can't find any sort of shape that fits it. Are there any 3D shapes with only faces that have coplanar matches with other faces in the shape? ...
0
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0answers
26 views

Motion tracking formula by tracking information

I have tracking information of a short clip that demonstrates a first person view flight. The red dot is a x,y tracking information of a specific point in the clip. Additionally, we have the angle, ...
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1answer
40 views

Turning two rotation groups into one

I need to figure out how to turn two rotation groups, each rotating around Z, X then Y into a single rotation group, so that in one set of rotations I might obtain the same positions for a set of ...
5
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3answers
121 views

Explain branches of geometry for non-mathematician

Some background - I'm an advanced physics undergrad and lately was motivated to self study basic contemporary geometry to get a better grip on general relativity (maybe there is a more appropriate ...
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1answer
56 views

Area of the figure within the circle and outside a polygon

For which values of the parameter $c \in \mathbb{R}$, the area $S$ of the figure $F$, consisting of the points $(x,y)$ such that $$\begin{gathered} \max \{ \left| x \right|,y\} \geqslant 2c \hfill ...
2
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1answer
45 views

Conversion between coordinate systems

I am trying to convert between two coordinate systems and think I've come up with the answer but would like to make sure my assumptions are correct and to help with some of the math. The problem is ...
3
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1answer
70 views

Why can't the nth triangular number be expressed as the area of an equilateral triangle?

It should be self-intuitive that the $nth$ triangular number is an equilateral triangle with base $n$, and thus its area should equal the value of the triangular number. So, I was wondering: why ...
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1answer
56 views

How to know which side of the right angled triangle is the base?

If we are given a right angled triangle without any angle or length of any side. How we will find that which side is the base, which side is the perpendicular.
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2answers
81 views

Extension of Descartes' “Kissing Circles” Theorem

Descartes' "Kissing Circle" Theorem relates the radii, $r_1$, $r_2$, $r_3$, $r_4$, of four mutually-tangent circles thusly: $$( k_1 + k_2 + k_3 + k_4 )^2 = 2 ( k_1^2 + k_2^2 + k_3^2 + k_4^2 ) ...
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0answers
15 views

Subset of Jordan set of positive lebesgue measure

let $T \subset \mathbb{R}^d$. Given on $T$, a Jordan set of positive Lebesgue measure, $l(T)>0$ . Let a set $M \subset T$; with $l(M)=0$. Please explain what is special about the set M. Has it got ...
0
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2answers
35 views

Triangle and Ratio : Find the length of a side.

Let $\theta = \angle CAD, \phi = \angle CDB, \varphi=\angle DBC, \alpha = \angle BCD$ and $\beta=\angle ACD$. Then we have the following system of equations $\theta + \varphi = 90^{\circ},$ ...
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2answers
37 views

Why does the equation of a circle have to have the same $x^2,y^2$ coefficients?

In one of my geometry texts, it tells me they should be the same but not why. I am unsatisfied with this. Suppose that: $$ax^2+by^2 + cx + dy + f = 0 \text{ such that } a \neq b$$ is the equation ...
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1answer
44 views

How to prove for any point $P$ inside an equilateral triangle $ABC$, $PA+PB > PC$ [closed]

Prove that, for any point $P$ inside an equilateral triangle $ABC$ , $PA+PB \gt PC$.
2
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2answers
59 views

Trying to understand the limit of regular polygons: circle vs apeirogon (vs infinigon?)

In the definition of regular polygon at the Wikipedia, there is this statement about the limit of a n-gon: "In the limit, a sequence of regular polygons with an increasing number of sides becomes ...
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0answers
22 views

Suppose from the point P (m,n) two tangents PQ & PR are drawn to the points Q & R on the circle [x^2+y^2=a^2].Then find area of triangle PQR .

Suppose from the point $P = (m,n)$ two tangents $PQ$ and $PR$ are drawn to the points $Q$ and $R$ on the circle $x^2+y^2=a^2$. Find area of $\triangle PQR$. The information related to this ...
2
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0answers
21 views

can't figure out multilateration with xyz positions of each post and difference in time

I'm having some real issues figuring out multilateration. I'll start by saying I'm not a math whiz, but I am usually able to figure most things out, but this one has been throwing me through a loop ...
1
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1answer
70 views

One Square and one straight line(pipe) [closed]

Edited: A farmer has a farm.The farm is a square whose sides have length 1. A single straight water pipe passes somewhere under the farm with depth one meter. He wants to dig furrows to find the ...
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0answers
28 views

A question about possible differences between plane and spherical geometry

Are the theorems about Brocard points and the Brocard angle of plane triangles also true for spherical triangles?
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0answers
23 views

How many grams of coating is being yield per volume width?

The cylinder is 8.00 inches in diameter and 4.940 inches in width. 1.500 inches in width has a volume of 15. 3.440 inches in width has a volume of 12. The total grams of coating yield from the both ...
1
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0answers
36 views

How much heigth can a roll of pipe insulation cover?

I'm getting a bit confused on calculating how much insulation I need to buy. Here are the specs of the insulation: Dimensions: $1.5''\times 24''\times 25'$ Packaging: $50$ square feet per roll The ...
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0answers
54 views

Difference between exponential maps composed with parallel transport along two different geodesics?

Let $(M,g)$ be a Riemannian manifold, and let $\gamma_{p,v}, \gamma_{p,w}$ be two geodesics starting from $p$ with directions/initial vectors $v,w$ respectively. Consider the two operations (to be ...