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

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1
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1answer
109 views

Sum of angles in a polygon - Alternative solution

I was fascinated by this problem from the first moment I saw it. Let $P$ be a convex polygon which has no two sides which are parallel. Each side $A_iA_{i+1}$ has a furthest away point $C_i$. ...
-4
votes
3answers
125 views

Construct point P 4.2cm from A and 5.6cm from B

A and B are 2 points 7cm apart. Construct the positions of point P which is 4.2cm from A and B 5.6cm from B. How many possible positions for P are there. Measure the distance between them.
2
votes
2answers
77 views

Geometry Parabola $2x^2+\alpha x+3\alpha$ to find common point

Can you help me find the answer to this question? For any real number $\alpha$, the parabola $f_{\alpha}(x) = 2x^2 + \alpha x + 3\alpha$ passes through the common point $(a, b)$. What is the value ...
3
votes
0answers
71 views

Curvature on topological spaces

On what subsets of the category of topological spaces are different notions of curvature defined?
0
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1answer
72 views

a problem of Geometry

in Tetrahedral ABCD : E,F and G are to order Middle of sides AB , BC, AD . also GE is Perpendicular to AB and GF is Perpendicular to BC . if angle of ABC is 96 degree . calculate angle of ACD?
9
votes
1answer
870 views

How to understand spectral decomposition geometrically

Let $A$ be a $k\times k$ positive definite symmetric matrix. By spectral decomposition, we have $$A = \lambda_1e_1e_1'+ ... + \lambda_ke_ke_k'$$ and $$A^{-1} = ...
2
votes
0answers
74 views

Graphs that “polygonize” a manifold

It's rather easy to conceptualize a covering of the Euclidean plane by a countable set of convex but otherwise arbitrarily sized and shaped polygons (seen as subsets of the plane) without overlaps. It ...
5
votes
1answer
161 views

symmetric matrices that aren't diagonalizable by a SPECIAL orthogonal matrix

Is there a $2\times 2$ symmetric matrix that can't be diagonalized by a special orthogonal matrix? The spectral theorem guarantees an orthogonal matrix, but both the algebra and the geometry suggest ...
3
votes
2answers
259 views

Convex polygons partitioned into concave quadrilaterals

I found the following problem: Is it possible to partition every convex polygon into a finite number concave quadrilaterals? The answer seems negative, because heuristically if we remove a ...
0
votes
1answer
227 views

making three parallel lines (3d) with equal distance seperation

I have three parallel lines (3d lines). say AB, CD, EF. The center line i.e. CD is given by intersecting the two planes by which the AB, DE lie on. The shortest distance between AB and CD (say d1) is ...
0
votes
1answer
21 views

length of c when calulating using sines

I cannot understand how i get a negative answer. I have a triangle with three angles and one side. To get another side $c$ I used the below calculation but got a negative answer. Given that ...
3
votes
2answers
4k views

Solving Right Triangle Given Two Sides

I have a right triangle whose base has length 40 cm and whose hypotenuse has length 43 cm. How can I determine the height and the measures of the remaining two angles?
3
votes
1answer
224 views

Quadrilateral geometry

It's given distance between $AB = 27$ $BC = 752$ $CD = 26.75$ $AD = 758$ $CE = 1$ $0 < FC < 752$ How do I find $FG = x$ for point $F$ on line $BC$? Is it even possible? EDIT: As André ...
0
votes
1answer
92 views

Closest Packing of Spherical Caps

Let the surface $S_n$ of the unit ball in $\mathbb{R}^n$ centered at the origin $O$ be defined as the set of points $P(x_1,x_2,…,x_n )$ such that $x_1^2+x_2^2+⋯+x_n^2=1$. Let the spherical cap $C(α)$ ...
0
votes
1answer
120 views

compute overlapping % of 2 parallel lines

I have two parallel line segments, say AB, CD. If I project the end points onto a common third parallel line, then I want to know the portion of overlap made by above 2 lines. I think I should ...
3
votes
2answers
267 views

Proving Similar triangles using SSS

I am trying to prove that the following triangles are similar. Following information is given in this regard: AB, AC & median AD of triangle ABC are respectively proportional to PQ, PR & ...
1
vote
2answers
4k views

What is the maximum volume of a cylinder that can fit in a sphere of a constant radius?

The first question that comes into my mind here is whether any cylinder that touches(at 4 pts) the circumference of the sphere and does not go out of it, has equal volume? Second, how do i ...
3
votes
4answers
2k views

Find an angle in a given triangle

$\triangle ABC$ has sides $AC = BC$ and $\angle ACB = 96^\circ$. $D$ is a point in $\triangle ABC$ such that $\angle DAB = 18^\circ$ and $\angle DBA = 30^\circ$. What is the measure (in degrees) of ...
2
votes
1answer
583 views

Kinect skeleton scaling in 3d space

I am developing a physioterapy system with kinect and need to scale a skeleton size to another skeleton size. The kinect sensor recognizes 20 body joints, of every joint i have the x, y, and z ...
3
votes
0answers
740 views

Geometry Proof: Convex Quadrilateral

A quadrilateral ABCD is formed from four distinct points (called the vertices), no three of which are collinear, and from the segments AB, CB, CD, and DA (called the sides), which have no ...
1
vote
1answer
233 views

Circular motion “calculate the angle”

I have a equation i need to find out how they hang together. angel = (velocity * time) - (acceleration * time * time / 2) I know circumference of a circle: ...
4
votes
2answers
119 views

surface unit sphere

Suppose $\sum_i c_i = 0$ and $Z$ is random draw from the collection of unit vectors, i.e. it has Euclidean norm $\lVert Z \rVert = 1$. Of course $E\left[\sum_i c_iZ_i^2 \right]=0$. What can we say ...
1
vote
1answer
218 views

Uniqueness of shortest distance between the center of two circles (and in higher dimensions)

I am an EE presently writing a book on microwave semiconductors. In one of the common graphs we employ - the Smith chart - we use the bilinear transformation to map rectangular regions to circles in ...
2
votes
0answers
38 views

Sphere-Packing for Cubeoctahedra

Please verify that the following information is correct: The way to pack 13 spheres (with equal diameter), 12 around a 13th in the center, together so that they are all in contact with each other ...
1
vote
0answers
51 views

Planar quadrangle $ABCD$ satisfy $AB = BC$ and $CD = DA$. Compute a point $P$ such that $PA+PB+PC+PD$ is minimum

Let a planar quadrangle $ABCD$ satisfy $AB = BC$ and $CD = DA$. Compute a point $P$ such that $PA+PB+PC+PD$ is minimum, for each of following two cases. The inner angle of $B$ is greater than $\pi$ ...
1
vote
1answer
481 views

Calculate ellipse diameters with five points (center point and four other).

Is it possible to calculate radii (or diameters) of ellipse given: ...
5
votes
3answers
318 views

On Ceva's Theorem?

The famous Ceva's Theorem on a triangle $\Delta \text{ABC}$ $$\frac{AJ}{JB} \cdot \frac{BI}{IC} \cdot \frac{CK}{EK} = 1$$ is usually proven using the property that the area of a triangle of ...
1
vote
1answer
255 views

Equivalence between algebraic statements and geometric relations.

I'm currently trying to read a geometry and symmetry book and came across a little problem that I am having difficulty understanding. I need to show that if xm=mx then the point X is on the line M, ...
2
votes
0answers
51 views

Isomorphism of $P(V)$ and $P(V^*)$

Let $V$ be a finite-dimensional left vector space over a division ring $K$, and let $V^*$ the dual right vector space (consisting of all linear functions from $V$ to $K$). We can (and will) treat ...
2
votes
1answer
100 views

Projective planes over division rings sef-dual?

My question is this: Is the projective plane $P(K^3)$ (the points are the one-dimensional subspaces and the lines are the two-dimensional subspaces) for a division ring $K$ isomorphic to its dual? I ...
1
vote
0answers
147 views

Area of ring section closed within a rectangle

I wish to find out the area of a section of a ring which can be acted on my a rectangle 100mm wide by 60mm height. I know the inner diameter,ID and outer diameter,OD of the ring and the width of the ...
0
votes
1answer
214 views

3 Dimensional Geometry

Greedy Geoff sawed off a corner of a brick shaped block of Christmas cake, exposing a triangular fresh face of moist rich delicious gateau. He placed the tetrahedral fragment on the table, with its ...
2
votes
1answer
187 views

Altitude of tetrahedron?

I'm really curious to know any relationships between the altitude of a tetrahedron and how the foot of this altitude splits the base triangle. For example if you have a tetrahedron PABC with apex P, ...
3
votes
2answers
203 views

Pythagorean theorem in unitary vector spaces

In euclidean (i.e. real) vector spaces the pythagorean theorem holds, i.e. $$ ||x+y||^2 = ||x||^2 + ||y||^2 \Leftrightarrow x \perp y. $$ But for unitary (i.e. complex) vector spaces it fails because ...
1
vote
1answer
202 views

scale and ratio : try to find x,y,width,height

http://i.stack.imgur.com/LbQSu.png I have to boxes with same ratio. How can I find position x,y and width,height in the second box ?
0
votes
1answer
88 views

What is the parametric value t' for an ellipse that corresponds to the same angle t in an inscribed circle?

I have a unit circle centered at the origin defined parametrically as $$ x = \cos \ t,\ y = \sin \ t $$ and an ellipse centered at the origin defined parametrically as $$ x = a\cdot \cos \ ...
0
votes
1answer
135 views

Parabolas and projectiles

Given $2$ points, $A$ and $B$, if I am in $A$ and I have an inclination angle $c$, with how many velocity do I need to shoot a projectile to hit $B$ ? My problem is, how do I setup this data in an ...
3
votes
0answers
96 views

How to model bending, folding of 2D figures?

2D shape can be folded in various ways. For example, trapezoid can have its sides (with the acute angles) folded, so that it will effectively become rectangle – with the difference, that part of the ...
2
votes
1answer
151 views

I have a vector of length 1, and two angles (in $xz$ plane and $yz$ plane), how do i get the $x,y,z$ compontents of this vector?

I just can't see what's wrong, this should be relatively simple... I have a vector which has length 1. Then, I have two angles. The first ($\gamma$) is the angle between the projection of the vector ...
1
vote
2answers
289 views

Triangle in hexagon

In a regular hexagon ABCDEF is the midpoint (G)of the sides FE and S intersection of lines AC and GB. (a) What is the relationship shared point of straight ...
0
votes
2answers
84 views

Finding An Equation For A Parabola

The information given in this particular problem: Axis is parallel to y-axis; graph passes through and $(4,11)$.$(3, 4)$ $(0,3)$ From this information, I know that it opens either upwards or ...
-2
votes
2answers
159 views

Can it be argued that this question only has 1 answer ultimately?

I came across this quiz question in a forum today. I would like to ask for your opinion of this notorious mathematics question, and also, to share. This question came out in Singapore's PSLE ...
3
votes
0answers
66 views

Is there a way to derive the surface of a ball without integral? [duplicate]

Possible Duplicate: Can the Surface Area of a Sphere be found without using Integration? A ball is effectively a pyramid with "curved" based. If we know the surface, which is $O=4 \pi r^2$, ...
0
votes
1answer
260 views

What are spatial Transformations?

What are spatial Transformations? Are Affine transformations also part of spatial transformations?
1
vote
3answers
587 views

What is the maximum number of regions produced, i.e. $f(n)$, by joining all vertexes with line segments of a convex polygon with $n$ sides?

What is the maximum number of regions produced, i.e. $f(n)$, by joining all vertexes with line segments of a convex polygon with $n$ sides? For example, for the hexagon on the left, number of ...
1
vote
2answers
61 views

Determine whether the triangles $ABC$ and $DEF$ are rectangles

How can we determine whether the triangles $ABC$ and $DEF$ are rectangles? We have $A(-6,5),B(-3,3),C(1,9),D(1,3),E(5,1),F(11,10)$.
1
vote
2answers
129 views

finding area of the fourth circle

Three circles of the same radius are arranged in such way that one circle is tangent to the other two. A fourth circle is drawn so that it will contain three circles and be tangent to the other ...
1
vote
1answer
43 views

Why does this system of equations result in an always-positive output?

I have two variables, M and P, whose relationship is described by the following two equations: [1] P = 50.5 * M / ( M - 50) [2] M = C * P where C is a positive ...
4
votes
2answers
471 views

Construct a triangle given one side, its height and inradius

I've been scratching my head with this problem: "Draw a triangle given one of its sides, the height of that side and the inradius." Now, I can calculate the area and obtain the semiperimeter. From ...
2
votes
4answers
1k views

what's the name of the theorem:median of right-triangle hypotenuse is always half of it

This question is related to one of my previous questions. The answer to that question included a theorem: "The median on the hypotenuse of a right triangle equals one-half the hypotenuse". When I ...