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

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Distance covered by point on the rim

Given a circular wheel that is rotating at the rate of $25$ revolutions per minute. If the radius of the wheel is $50 \space cm$, what could be the distance covered by a point on the rim in one second ...
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2answers
392 views

Ways to define a curve

I'm trying to give shapes in my physics engine roundness/ curvature. I am aware of various methods for mathematically defining curvature such as bezier-curves, ellipses, etc; but I'm not sure which ...
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1answer
736 views

Calculating Intersection of an Ellipse and a Line

I found this page which gave me some equations on solving the intersection of a line with an ellipse given a point on the line and the slope of the line: There Isn't much explanation but ...
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2answers
271 views

How to calculate circumference of circle in $L^p$?

I want to find the circumference of a circle as a function of its radius in $\mathbb{R}^2$ with $l_p$ metric. Is the following anywhere near correct for radius $r$? $$ C_p(r) = 4\int_0^r \sqrt{1 + ...
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3answers
2k views

How to get the limits of rotated ellipse?

The box that an ellipse fits is easily calculated if there are no rotation, or if the rotation is ${x*90^o}$ (where x is an integer) is easy. For a (major radius) and b (minor radius), it is : ...
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2answers
155 views

Equal division of rectangles to make total?

I want to specify a number and have that number halve itself equally so that the bottom of my canvas fills with rectangles. For instance, if I specified the number 4, the bottom of my canvas would ...
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2answers
393 views

How to compute the volume of the polyhedron with vertices at centre of a cube?

The centers of the faces of a cube are also the vertices of polyhedron. How to Compute the ratio of the volume of the polyhedron to that of the cube containing it?
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1answer
213 views

Finding the position of a person on a grid, when you know the $(x,y)$ coordinates of transmitters and the signal strength at the person

I have a $100\times100$ grid. I have a transmitter on each corner, $4$ in total. $$\begin{array}{rl}\text{Transmitter (a) is at}&(0,0);\\ \text{(b) is at}&(100,0);\\ \text{(c) is ...
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1answer
48 views

Decreasing $y$ value in a triangle

I'm having trouble with this basic math question. Any hints? Given a graph with lines $x=y$ and $x+3y=4$. Consider the triangle formed by these two lines and $y=0$. When $y$ is increasing from $0$ ...
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3answers
187 views

Is it possible to inscribe a regular tetrahedron in every convex body?

Is it possible to inscribe at least one regular tetrahedron in every convex body?
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1answer
4k views

Calculating Distance of a Point from an Ellipse Border

I'm thinking about using oriented ellipses to represent curves (dents/bumps etc.) in my physics engine, and have a few questions about working with them: What methods are there to finding the ...
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1answer
142 views

Five tangent circles inscribed in the same angle

Given: Five circles have been inscribed in an angle (their centers are contained in the angle bisector). Adjacent circles are tangent. Express the radius of the middle circle in terms of the radii of ...
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1answer
167 views

A semi-Riemannian geometry exercise

How can I prove that there are no compact semi-Riemannian hypersurfaces in semi-euclidean space $\mathbb{R}_v^n$ of index $v$ with $0<v<n$??. Thanks for any help!!
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1answer
474 views

Minmax problem for polygons

Let $\text{Pol}_n$ be the set of all convex polygons on a plane with $n$ sides. For $P\in \text{Pol}_n$ denote by $\text{Tr}(P)$ the set of all triangles whose vertices are some vertices of $P$. I ...
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3answers
238 views

Isometries of $\mathbb{R}^3$

So I'm attempting a proof that isometries of $\mathbb{R}^3$ are the product of at most 4 reflections. Preliminarily, I needed to prove that any point in $\mathbb{R}^3$ is uniquely determined by its ...
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2answers
664 views

Calculating position along the hypotenuse

The blue dot moves, I know its x and y coordinates, and I also know that that causes the red dot to move along the triangle's hypotenuse in such a way that the red dot's y coordinate is always equal ...
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2answers
11k views

How can I calculate the centroid of polygon?

What is the way to calculate the centroid of polygon? I have a concave polygon of 16 points, and I want know the centroid of that. thanks
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1answer
102 views

Polyhedra with symmetries order three

If I have a natural number $o=2n$ or $4n$ I can create a polyhedron whose group of symmetries has order $o$ by making a polygon like $C_n$ and then dragging it out to make a prism (I believe this is ...
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2answers
389 views

Perspective problem - trapezium turned square

True or false: If you draw a trapezium on the ground, there always exists a point above (but not necessarily directly above) the trapezium such that the trapezium looks like a square from that point. ...
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2answers
6k views

How to multiply vector 3 with 4by4 matrix, more precisely position * transformation matrix

All geometry in computer graphics are transformed by position * transform matrix; The issue is the fact that position is a vector with 3 components (x,y,z); And transform matrix is a 4 by 4 with one ...
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1answer
74 views

Reconstruct shape of a body from rationality of its projections

There is a closed convex body $S$ in $\mathbb{R}^3$. Areas of its projections on all planes (not only those normal to axes $x,y,z$) are rational numbers. Can we deduce that $S$ is a ball? Replace ...
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3answers
1k views

Analytically compute signed distance of ellipsoid

I'm trying to generate a 3d signed distance field for a origin centered ellipsoid. For a sphere this is pretty easy: $$\sqrt{x^2 + y^2 + z^2}-r$$ where $r$ is the radius. I'm not sure what the best ...
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2answers
324 views

Help with solving speed/time/distance traversal problem

I'm not any sort of math wiz, and I've run up against a problem that is fairly complex for me to solve. A friend suggested this site might be able to provide some help. So let me try to describe the ...
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1answer
715 views

How can we prove the locus is a circle?

Given two fixed points A and B, find the locus of the point P, satisfying PA=2PB. Of course we can use Cartesian geometry to find the equation of the curve. Let the midpoint of A and B be the ...
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1answer
2k views

Translating an xy coordinate of a point from local coordinate system to global coordinate system

Can you please help me to figure out a way to obtain global coordinates of a point which is defined within local coordinates system. Known: (x,y) origin of the local coordinate system. angle of the ...
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2answers
59 views

Traveling across an arc?

So, I have an arc that's part of a circle that I must "travel across". The circle has a radius of $15$ - a circumference of $94.248$ (rounding). The arc length in question is equal to $15.708$. Now, ...
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1answer
240 views

A problem with an inscribed oval

This oval is made up of 4 arcs, 2 on the left and right sides of radius 1 and 2 on top and bottom of radius $R$. Given that the the oval fits in a $4 \times 8$ rectangle, is it possible to find $R$ ? ...
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2answers
338 views

Isosceles Trapezium problem

I came across a problem in a certain quiz which I couldn't solve. Here it is reproduced: Since $BX$ is midpoint of $AB$, $AB = CD = 2$ . Now $AD$ and $BC$ remain to be calculated. How can the right ...
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1answer
796 views

Integer coordinate set of points that is a member of sphere surface

I have a graphic application to develop which involve many spheres. I should determine then on run time. Supposing that I have a sphere of radius r, how can I determine the sub set of the sphere ...
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1answer
344 views

How to find the maximum & minimum possible Location within a graph?

For example, I have a graph having size of 480 width x 300 height. I am able to calculate the center point ( & that is 240,150 ). Now my question is as follows. I have a location/vertex on that ...
2
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1answer
1k views

Finding points which divides a right trapezoid's area into equal pieces

I have a right trapezoid as follows; We have $h$, $b$ and $a$. For any $n$, I need to divide total area of trapezoid into equal parts. I have to find a general formulation for the length of $p$ ...
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1answer
400 views

Need help with the proof of conic section

Prove that the intersection of a plane and a object consist of one cone and one upside-down cone where the tip of cone meet is either degenerate conic or conic Also, idenify in what situation, the ...
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0answers
73 views

Some question concerning curve of second order

Let $$F(x,y)=ax^2+2bxy+cy^2+2dx+2ey+f,$$ $$\phi(x,y)=ax^2+2bxy+cy^2,$$ $x,y \in \mathbb{R}$. Assume that for some $x_0, y_0 \in \mathbb{R}$ and for some $\alpha, \beta \in \mathbb{R}$ such that ...
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1answer
224 views

Trigonometry basic question

I am training Trigonometry just for fun, so I am not in a hurry, but would like to know how to answer this question - not the result, but how to do it. Sorry because I understand this is too basic for ...
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3answers
3k views

How do you find the distance from a point to a plane?

I am having trouble with this: Find the distance from the point $(1,1,1)$ to the plane $2x+2y+z=0$. Any ideas? Thanks.
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2answers
2k views

Parallelogram trigonometry

(Sorry for the ambiguous title, couldn't think of a better one) While leafing through a highschool textbook, I found what looked like an interesting question in trigonometry. My trigonometry skills ...
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1answer
227 views

Why are the coefficients of the base states of a qubit complex numbers?

Why are qubits represented as $$\left|{q}\right\rangle = \alpha\left|{0}\right\rangle+\beta\left|{1}\right\rangle\equiv\alpha\left[{1 \ 0}\right]^T+\beta\left[{0 \ 1}\right]^T; ...
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0answers
33 views

Proving the regularity of the pyramid

In the pyramid of base ABC and the apex S the heights AA', BB', CC', SS' cross in one point lying within the pyramid. Point O is the center of the sphere circumscribed on this pyramid. Prove that if ...
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2answers
91 views

Help with a geometry problem

The problem says: A triangle has its lengths in an arithmetic progression, with difference d. The area of the triangle is t. Find the dimensions. the solution says: the notation can be even better if ...
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2answers
275 views

Questions regarding the projective space

In geometry, we have (kind of) introduced the projective space. Sadly, I have problems understanding some connections and I hope somebody here might help me out, as wikipedia's entry and my ...
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1answer
56 views

Circles with centers in points

Find all $n\geq2$ such that we can have n points $p_i$, and n circles $C_t$, such that if $j\neq k$, then $p_j$ is contained in $C_k$, and each $C_q$ has a point $p_q$ at its center. Could you please ...
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0answers
128 views

Why is the circumference (of a circle) proportional to its radius? [duplicate]

Possible Duplicate: Proof that Pi is constant (the same for all circles), without using limits How can you prove that the ratio of the circumference to the radius is a constant (regardless ...
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1answer
2k views

Arbitrary Quadrilaterals

what is an arbitrary quadrilateral? I can't find a definition of it anywhere. How would you find the area of an arbitrary quadrilateral?
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1answer
111 views

Computing the point which is closest to many Planar surfaces

Suppose, i have been given different planes which orients to different direction (i.e. i know only the plane parameter of those planes). If i am able to find out planes (probably more than 3 planes) ...
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2answers
140 views

Rotating between $3$D frames

Given two frames, is it possible to compute any rotation of the form $$R = R_xR_yR_z $$ that would tranform the frame $A$ into the frame $B$? the rotation will be described by Euler angles as I ...
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1answer
176 views

The definition of the curve?

What is the definition of the curve? a. Is the image of $x^2+y^2=1(x\neq0)$ a curve? b. Is a point a curve? Here are the definitions I found in Wikipedia that may help. A curve is a topological ...
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1answer
135 views

Solid whose rotational symmetry group corresponds to $\textrm{SO}(2)\times \mathbb{Z}_2$

Sorry to inundate the feed with a question quite similar to my last, but again I've been drawing pictures for quite a while with little success. Does anyone have any idea how to represent the product ...
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1answer
580 views

Angles for a great dodecahedron

Could someone describe to me how to find the angle between two intersecting pentagonal faces on a great dodecahedron? Thanks
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1answer
187 views

Set of points with unique distances

Is there a set of points in $\mathbb{R}^n$ such that every positive distance is realized by exactly one pair of points in the set? I can see that if it exists, the set must be uncountable and ...
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1answer
528 views

Union area of circle and triangle

Having circle placed in $xi;yi$ coords with radius $r$ and also having three verticles of the triangle how can we calculate union area of this circle and triangle? Seems like it required basic ...