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

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0
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2answers
137 views

metric preserving transformations (isometry)

Maybe it will be very general question but i wonder what is the importance of metric preserving transformations? Where can we use this concept in mathematics?
12
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8answers
694 views

Cleverest construction of a dodecahedron / icosahedron?

One can show, as an elementary application of Euler's formula, that there are at most five regular convex polytopes in 3-space. The tetrahedra, cube, and octohedra all admit very intuitive ...
1
vote
1answer
6k views

finding sides of a triangle when circumradius and inradius are given

The radius of the circumscribed circle of a right triangle is $15 cm$ and the radius of its inscribed circle is $6 cm$. Find sides of triangle. From another site I got, $c=30$, $a+b=2(15+6)=42$. ...
0
votes
1answer
49 views

Find the maximum volume

In the sphere of radius 3 is inscribed simple cone. What is the maximum volume of such a cone ? I have no idea how to find the max volume, I can consider only cone with right angle between the arms ...
1
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1answer
1k views

Calculate Ellipse From Points?

How can I calculate an ellipse from a group of points ? Result: center point, x-radius, y-radius ? I'm not mathematician so I don't really know the best parameter style for ellipses. This ellipse ...
8
votes
4answers
637 views

Must a curve of constant width be generated with an odd number of sides?

From what I have seen (and to some extend read), a curve of constant width generated from a polygon with an even number of sides is not possible. Wikipedia cites an Oxford University paper when it ...
1
vote
2answers
146 views

Calculate geometry created by “slicing” rectangle with lines

Given a rectangle with a series lines intersecting it, how would you calculate the points of each individual shape created? In this particular application that we are working on, the user can "slice" ...
4
votes
2answers
232 views

Quadrilateral geometry problem, couldn't solve it.

So, I got this question a little while ago and couldn't see how to solve it. The problem follows as such: "In the following figure, G is the midpoint of CD and I is the midpoint of GE. BE:EA = 4:1 and ...
3
votes
6answers
599 views

Diophantine quartic equation in four variables

Comments from a recent Question, Cyclic quadrilateral with equal area and perimeter, ask about such cases with (positive) integer lengths. Using Brahmagupta's formula for the area of a cyclic ...
2
votes
1answer
259 views

classification of quadrics

Consider the projective plane $\mathbb{R}P^2$ and a symmetric matrix $B \neq 0$ of a bilinear form that defines a quadric $Q := \{ [v] \in \mathbb{R}P^2 : v^tBv = 0\}$. Is the following ok? And for ...
0
votes
1answer
54 views

Characteristics emerging from subdividing an obtuse scalene triangle?

I'm relying only on the geometry I learned in high school. Given a scalene obtuse triangle $ABC$, where $AC$ is opposite the obtuse angle, and a point $D$ in $AC$ such that $AD = DC$ (a midpoint). ...
2
votes
3answers
115 views

Separating $3n$ points on the plane by a line

I am trying to solve a problem in geometry (a contest-type question), and I wondering if the following result is true. (If it is true, then it makes life much easier!) Suppose there are $3n$ ...
0
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1answer
108 views

Intersection of conics

By conic we understand a conic on the projective plane $\mathbb{P}_2=\mathbb{P}(V)$, where $V$ is $3$-dimensional. I'd like to ask how to find the number of points in the intersection of two given ...
0
votes
1answer
95 views

Reflect a point vector in a conical surface and determine average resultant vector.

Consider a point $P~(P_x,P_y,0)$ which lies somewhere in the Cartesian region $x > 0. $ Consider a simple 3D cone surface with half angle $\gamma$, originating at point $\mathcal{O}$ $(0,0,0)$ ...
0
votes
4answers
122 views

Given Two Lines, How to Find a Point on Line $2$ given a Specific Distance From Line $1$?

I have two lines (U and V). What is the method to calculate a point on V given a specified distance (d) from U? The lines may be assumed that they do intersect (are not parallel) and are straight ...
2
votes
1answer
285 views

A proof of an interesting Geometric Vector Theorem.

Suppose $O$ is the centre of the circumscribing circle of triangle $ABC$ and $H$ is its orthocentre. Prove that vector $OH$ is equal to the sum of the vectors $OA$, $OB$ and $OC$. An answer I ...
0
votes
1answer
67 views

Show that the image of Gaussian map of a generalized cone is a curve on $S^2$ and deduce that the cone has zero Gaussian curvature.

Show that the image of Gaussian map of a generalized cone is a curve on $S^2$ and deduce that the cone has zero Gaussian curvature. I dont have enough idea. Please explain the question clearly. ...
0
votes
2answers
119 views

point A is equal distance away from the Y axis and B point . What will be the value of k?

Lets we have a coordinates in the Y axis. Let we have another coordinate A(5,k) which is equal from the Y axis and a cordinate B (2,3). How to find out the k? I have evaluated the distance then, ...
4
votes
3answers
184 views

Proof that a line cuts in half the area of a parallelogram iff it goes through the intersection of the diagonals?

I read a theorem in a book which says that a line bisects a parallelogram iff it goes through the intersection of the diagonals. The edge case of this is of course if the line is one of the diagonal ...
0
votes
1answer
143 views

vectors in 3D space and Right-Hand Rule

Suppose we have three vectors in 3D space. My questions are: How we check if these vectors are satisfy the right-hand rule or not. I know that it's possible to make the three vectors satisfy the ...
2
votes
0answers
169 views

How is Euler-Lagrange equation used to find optimal solutions in minimizing a function?

How is the Euler-Lagrange equation: $$ L_x(t,q(t),q'(t))-\dfrac{d}{dt}L_v(t,q(t),q'(t))=0 $$ used mathematically in finding the optimal solutions of minimising a function? Can someone give me an ...
1
vote
0answers
70 views

Help with Plateau's Laws

Can someone please explain mathematically what is meant by the term 'smooth' in Plateau's First Law: "Soap films are made of entire smooth surfaces" Thank you in advance!
2
votes
0answers
59 views

Existence Of Congruent Triangles

Two triangles $ABC$, $XYZ$ are "good" when $AB=XY$, $AC=XZ$, $\angle ABC=\angle XYZ$. That is, when two segments are equal and a not-included angle is equal, they are "good". There are $n$ ...
3
votes
1answer
169 views

How to find the number of intersections of diagonals in icosahedron?

How to find the number of points of intersection of the diagonals in icosahedron?
0
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1answer
73 views

find a point in 3D space

Suppose we have $3$ fixed points $P_1, P_2, P_3$ in $3$-D space, their coordinates are $(x_i, y_i, z_i)$ for $i=1,2,3$. The problem is to find a point $P$ so that the distances from $P$ to ...
0
votes
1answer
84 views

Locus in the complex plane given an equation

I have the question Let $a$ and $e$ be two positive real numbers, with $0 < e < 1$. Describe the locus of the points $z$ in the complex plane which satisfy $|z - ae| + |z + ae| = 2a$. I ...
1
vote
2answers
1k views

How to find 2 unknown components of 3 collinear 3D points?

I've been given the question "The points A(5,-3,z), B(1,3,11) and C(x,15,27) are collinear. Find the values of x and z." However, the course material only covered proving collinearity of two ...
0
votes
3answers
1k views

How do I find the 3 possible 4th points when given 3 unnamed vertices of a parallelogram?

So, I got have this task: "The points (3, -4, 5), (1, 0, 5) and (3, 1, -2) are three of four vertices of parallelogram ABCD. Explain why there are three possibilities for the location of the ...
3
votes
1answer
221 views

How to project a polygon on an axis.

I'm trying to learn the Separating Axis Theorem, for my programming. I'm making a simple 2D game an I need this as a way to detect wether two polygons are intersecting. Problem is, I suck at math. ...
7
votes
4answers
4k views

The dot product of two vectors.

(Sorry for my very basic knowledge, I don't know much about math :) ). I understand how to calculate the dot product of the vectors. But I don't actually understand what a dot product is, and why ...
0
votes
1answer
389 views

How to get perpendicular line to an edge of a polygon.

This is a pretty basic geometry question, but I couldn't find an answer clear enough for me on Google (I don't know much about math). Let's say I have a rectangle. I have the coordinates for the four ...
0
votes
1answer
57 views

Bicentric quadrilaterals

I'm trying to prove that a 'tangential' quadrilateral (i.e. one with an in-circle) whose area is given by Brahmagupta's formula for a cyclic quadrilateral is also cyclic (and thus 'bicentric').
0
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1answer
36 views

A Question on tangential quadrilateral

Consider this tangential quadrilateral Is there any relation between angle $\angle XOY$ with sides $b2$ or $a2$ ?
0
votes
1answer
104 views

What's this called, and how do you do it mathematically?

So, I'm teaching myself physics, and I have limited knowledge of calculus(I'm taking my first high-school class next semester in math). I'm attempting to calculate torque, but this is math, not ...
2
votes
2answers
2k views

Surface area of intersection of two cylinders

Let $$R=\{(x,y,z):y^2+z^2\leq 1\,\, \text{and}\,\, x^2+z^2\leq 1\}.$$ Compute the volume of $R$. Compute the area of its boundary $\partial R$. I'm fine with #1. For #2, I have a ...
1
vote
1answer
133 views

Derivation of the length of an arc formula

My textbook says that the radian measure of an angle is the ratio: $\theta = \frac{s}{r}$ Where s is a portion of the entire circumference, and r is the radius. So essentially the arc length is thus: ...
5
votes
1answer
2k views

How to calculate width of Trapezoid at any point

I am working on a Guitar application and so have a trapezoid as the fretboard. I am currently writing code to display the frets along the fretboard, but am stuck trying to calculate what the width is ...
0
votes
2answers
165 views

How to do the Math behind Two Body Problem

Ok So, I recently checked out Lazy Foo Tutorials for SDL 1.2, and I read the tutorials. I want to program a 2 body problem onto the screen. So where the user enters the data for both body, velocity, ...
3
votes
2answers
913 views

Prove that two lines are perpendicular in isosceles triangle geometrically

We have given isosceles triangle $ABC$ with baseline $AB$. Point $M$ is midpoint of AB. Draw perpendicular line to side $AC$ through $M$ which intersects $AC$ in point $H$. Let $P$ be midpoint of ...
3
votes
0answers
68 views

Determine maximal surface area in given square (geometrically)

We have given square $ABCD$. Line $p$ through point $A$ intersects side $DC$ in point $Q$. Where on side $AB$ should we select point $M$ and where on side $BC$ point $N$ such that line $MN$ is ...
0
votes
3answers
576 views

Competition Math Geometry Problem

Note: I am paraphrasing this problem Consider a quadrilateral with 3 sides of equal length, and one longer side. This quadrilateral also has equal diagonals, both of which are equal in length to the ...
0
votes
1answer
128 views

Constructing image under homography from known information

If $f$ is a homography of the real projective line, $f^2=id$ (is an involution), and $f$ has exactly two fixed points, how can I construct (geometrically) the image of an arbitrary point?
1
vote
2answers
72 views

Is point exist in circle?

Let us consider x and y is a point and then make a radius of some value r.If suppose i had a ...
3
votes
3answers
192 views

Calculate area of a specific part of a circle?

I am trying to calculate the area of a specific region inside a circle. The region, in this case, is the green area inside the circle. The given material is the equation, radius and the center of ...
2
votes
1answer
409 views

Can I define a plane given 2 points in xyz coordinates as well as roll angle about that vector?

I am working on a complex motion analysis, trying to calculate wrist angles in 3 dimensions. I have sensors placed as this diagram depicts and need both flexion/extension angles as well as ...
0
votes
1answer
226 views

Finding angle on an inclined plane

How can I go about finding the angle, theta, in this Physics problem? As you can tell, the right-most triangle is a simple 30-60-90 triangle, so above the right angle is a 60deg angle. Then the ...
2
votes
3answers
180 views

Generalization of angle bisector to tetrahedron

Let $I$ be the center of the inscribed sphere of a tetrahedron $ABCD$ and let $I_A$ be the length of the line passing through $I$ from the vertex $A$ to the opposite face. I am looking for a formula ...
2
votes
1answer
421 views

Cyclic quadrilateral with equal area and perimeter

I was studying about cyclic quadrilaterals , and a thought came that are there infinite number of cyclic quadrilaterals having perimeter equal to its area or if they are finite and how many are there ...
0
votes
1answer
34 views

what $h_a$ in this triangle question.

Square $PQRS$ is inscribed into $\triangle ABC$ so that vertices $P$ and $Q$ lie on sides $AB$ and $AC$ and vertices $R$ and $S$ lie on $BC$. Express the length of the square’s side through $a$ and ...
3
votes
1answer
615 views

vector projection on a unit ball

On an article I'm reading, I find that: if $v$ is a vector, the projection of of $v$ on the unit ball is: $$p(v)=\frac{v}{\max\{1,\|v\|\}}$$ I know that a projection of a point $v$ into a space is the ...