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

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3
votes
1answer
51 views

Find center of sphere given only points inside sphere

This is not homework, and I don't even know if this is possible, but I'm curious: Given a list of points in Euclidean space, is it possible to find the center of a sphere that encompasses all of the ...
1
vote
2answers
33 views

Find the most distant points on a curve

Hy, I have to ask someone for help with this problem. I have a curve with this implicit equation: $$\left ( x^2 + y^2 \right )^2 = x^3 + y^3$$ I have to find the most distant coordinates from the ...
0
votes
1answer
30 views

Intersecting two circles using vectors

I'm trying to programmatically find the intersection points of two circles with different radii. Solving their equotations would be an option, but I thought of using vectors to do so. Assuming I ...
1
vote
0answers
25 views

Find the coordinates on surface of hemicube of polygons within same solid angle.

I'm stuck at the start of the problem. When the user asked to Enter inputs of $P_1(x,y)$ and $P_2(x,y)$ coordinates. I need to compute the coordinates of $P_1'(x,y)$ and $P_2'(x,y)$ from the figure ...
1
vote
0answers
33 views

How to solve the sets of equations to find the matrix of coefficients for an ellipsoid

Regarding the below question: Finding equation of an ellipsoid I have two more questions: 1- In the "update" section of answer provided by @achillehui I can not understand the method he described for ...
4
votes
1answer
39 views

Locating a radar in a plane

Given two located targets at $(x, y)=(- 2.0)$ and $(x, y)=(2,0)$. A radar, located in an unknown location of the $XY$ plane, and sends a pulse and in return receives pulses from the two targets. ...
2
votes
0answers
40 views

Drawing a Truncated Octahedron

I'm trying to draw a truncated octahedron in MATLAB. This is also known as a permutahedron so my strategy is to link up all the vertices via adjacent transpositions of permutations in $S_4$. What I ...
0
votes
0answers
10 views

Trilateration constraints

I am working for a positioning software experiment. I am asking here because the part i need to know for is about only Mathematics. I tried to visualize some sets of radius-coordinates combinations ...
4
votes
3answers
154 views

Geometric interpretation of an integral inequality

Let $f: [a, b] \to \mathbb [0, \infty)$ be an integrable function. By Cauchy-Schwartz: $$ \left(\int_a^b f(x) dx\right)^2 \leq (b-a) \int_a^b f(x)^2 dx$$ with equality iff $f$ is constant. If we ...
4
votes
1answer
51 views
+50

What series of 'hyperpolyhedrons' do exist? Is there an effective way to derive their cross-sections by 3-d subspace?

There are two obvious series of 'hyperpolyhedrons'. 'Hyperoctahedron' with vertices $(\pm1,0...0), (0,\pm1,0,...0)...(0,...0,\pm1)$ and each vertex connected by an edge with each other vertex ...
7
votes
4answers
174 views

Construction of a triangle

I need to construct a triangle with given information: $c = 6$, $h = 4$ and $\alpha - \beta = 30º$. I'll put approximate result for any clarification.
5
votes
1answer
68 views

Is $e$ involved in some geometric figure in any way?

Let's take some popular numbers in math: $\pi$, $e$, $\sqrt{2}$ and $\phi$. The number $\pi$ is the ratio between the circumference and the diameter of a circle; $\sqrt{2}$ is the length of a diagonal ...
1
vote
1answer
32 views

Variable Pitch Helices

Is it necessary for a helix to have constant pitch? If it is not so, what would be equation of a variable pitch helix?
0
votes
1answer
35 views

find the area of the triangle $ADB$.

$ABC$ and $ADE$ are two secants of a circle having radius $3$ units. Point $A$ is at a distance of $5$ units from centre. Secants includes an angle of $30$ degrees. If area of the triangle $ACE$ is ...
3
votes
1answer
32 views

Maximum area / perimeter ratio

With no limitation, to achieve the maximum area with a fixed perimeter, the shape is a circle, and the area / perimeter ratio would be $\frac{L}{4\pi}$ where $L$ is the perimeter lenght. However, if ...
0
votes
0answers
37 views

How find this minimum of the $|PA_{1}|+|PA_{2}|+|PA_{3}|+\cdots+|PA_{n}|$

Question: give the $n$ point $$A_{1}(x_{1},y_{1}),A_{2}(x_{2},y_{2}),A_{3}(x_{3},y_{3}),A_{4}(x_{4},y_{4}),\cdots,A_{n}(x_{n},y_{n}),x_{i}\in R,y_{i}>0$$ Find a ponit $P(x,0)$,such ...
0
votes
0answers
12 views

For an app teaching about polyhedra, what are some core characteristics to include?

For fun: I'm building a 3d app that teaches about polyhedra. What should I include? The obvious didactic elements for each polyhedron would be: Fundamental polygon's Vertices 
Edges
 Faces
 (and ...
5
votes
1answer
42 views

Proof of Incircle

A circle is drawn that intersects all three sides of $\triangle PQR$ as shown below. Prove that if AB = CD = EF, then the center of the circle is the incenter of $\triangle PQR$. Designate the ...
1
vote
2answers
37 views

Radius of a curvature

I have a lens (magnifying glass) and I want to calculate the radius of the curvatures on its sides. The lens in question diameter of the lens = 6 cm thickness at center = 7 mm thickness at edge = ...
7
votes
2answers
198 views

Hands of the clock, Revisited.

It has already been answered (here) that it is impossible for the (continuously moving) hands of a clock to trisect the face of said clock. Even ideally the hour, minute, and second hand can never ...
9
votes
1answer
66 views

Understanding Dynkin Diagrams - any organising ideas - are they now adequately understood?

Some 30 or so years ago JH Conway posed a question about the ubiquity of the Dynkin Diagram - not necessarily in public, but I heard him ask it. I think it was in the context of "what would be ...
0
votes
0answers
34 views

Farthest vector direction relative to other vectors

I wished to know the cheapest computational means (be it analytical or numerical) to find the vector from origin (normalised or not; I do not care about its magnitude) given any arbitrary set of ...
0
votes
1answer
23 views

Line varieties in Projective Geometry!

I'm an Engineering student. All of the sudden I need to know about "Family of Lines" which is a topic in "Projective Geometry". I've found the old book of Veblen & Young (and two other books) but ...
0
votes
1answer
28 views

length of secant line.

I'm looking for way to find the length of a secant line intersecting another line through the center of a circle with a known radius. The intersection point is on the circle and the angle between 2 ...
2
votes
2answers
53 views

What's the connection between “hyperbolic” inner product spaces and the hyperbolic plane?

In Jacobson's Basic Algebra I, in Kaplansky's Linear algebra and geometry and in Artin's Geometric algebra, a hyperbolic plane is defined to be a two-dimensional, nondegenerate inner product space ...
0
votes
1answer
50 views

Inscribed Circles in Triangles

This question appeared in this year's UNSW Maths competition. It was question 5b and it was the only question that i couldn't do. Sorry if my explanation is bad as it is complicated to understand ...
2
votes
3answers
60 views

Finding the equation of a line whose segment is intercepted between axes

The question is: Find the equation of a line through (-2, 5) and whose segment intercepted between axes in the 2nd quadrant is 7√2 I have two graphs in mind but I don't know which one is correct. The ...
0
votes
2answers
22 views

Find a point on a line that is also the third vertex of a triangle

I am interested in finding the $(x, y)$ coordinates for the point, $C$ in the figure below, which is also on the line showing going through the points, $B$ and $C$. I believe this problem has a unique ...
3
votes
1answer
48 views

Relationship between Surface Area and Volume

Question: Is there a general relationship between surface area and volume analogous to the below examples? Example 1. Consider a ball $B$ centered at the origin of a spherical coordinate system. The ...
0
votes
1answer
33 views

What is the length of the line joining the mid–points of PQ and RS for this given trapezium $PQRS$? [closed]

$PQRS$ is a trapezium, with $PQ$ parallel to $RS$. $PQ = 20$ cm, $RS = 3$ cm, $PQR = 30degree and $QPS = 60degree . What is the length of the line joining the mid–points of $PQ$ and $RS$?
1
vote
2answers
39 views

Parametrization of a surface

I am given the curve $ a (u) = (\cos(u), \sin(u), u) $. I am asked to write the parametrization of the surface obtained intersecting this curve with lines orthogonal to the z axis. How to do this? ...
-4
votes
1answer
50 views

Lines through vertices of regular hexagon and regular pentagon [closed]

ABCDEF is a regular hexagon and ABPQR is a regular pentagon of equal sides that are joined with each other through one common side AB. If the lines from neighbouring points of A (i.e. from F and R) ...
-2
votes
0answers
89 views

Imaginary curvature. [closed]

What would a shape with a curvature of $\Omega = \sqrt{-1}$ or $\Omega = i$ be? What would it look like, how many dimensions would it take up and is there a name such a shape, what would a geometry ...
0
votes
1answer
33 views

Solid Angle Integration

Can somebody explain the equivalence between integrating over the surface of a unit sphere and integrating over solid angle? I have been trying to understand the following transformation using a ...
0
votes
3answers
38 views

Finding the variable of a coordinate point on a circle

This might be a very simple question but I am having trouble figuring it out, so if anyone can explain: A circle is marked with three points A(-3,2),...
0
votes
1answer
27 views

Defining rotation without using angles, but as geometric transformations?

According to this article on angles, we can define rotation without using angles, and then use rotation to define angles. The relevant paragraph is at the very end: But what is a rotation? Is it ...
1
vote
2answers
23 views

Finding the points where a circle intersects an axis

A circle has the equation: x²+y²+4x-2y-11 = 0 What would be the coordinates of the points where the circle intersects with the y-axis and how would you calculate it?
3
votes
2answers
17 views

Radius of circumference tangent to square and circular sector

I would like to find the radius of the circumference shown in figure, knowing the side of the square is 5. I have decided to note said radius $r$ and the tiny diagonal bit not included in any circle ...
0
votes
0answers
21 views

Interior and exterior of a polygon in Hilbert axioms

First of all sorry for my bad English. Correct me if needed. I can't prove one theorem from Hilbert's "Foundations of Geometry". Here is the quote: Theorem 6. Every simple polygon, whose vertices ...
0
votes
3answers
32 views

How to find a 4D vector perpendicular to 3 other 4D vectors?

In 3 dimensions it is possible to find a vector c (one of infinitely many) perpendicular to two vectors a and b using the cross product. Is there any way of extending this to 4 dimensions, i.e. given ...
0
votes
1answer
62 views

Determine if one point lies between two other points on a sphere

My question is rather simple. Can I use the dot product to determine if a coordinate lies between two others? With coordinates I mean a Point P(latitude, longitude) on the surface of the sphere. I ...
0
votes
0answers
18 views

Every polyhedron $P \ne \mathbb{K}^n$ equals an intersection of finitely many half spaces.

Currently, I am reading some lecture notes on linear optimisation. I cannot see why the following (seemingly trivial) proposition holds. (How could I understand/proove it?) Every polyhedron $P \ne ...
43
votes
2answers
1k views

Geometry problem involving infinite number of circles

What is the sum of the areas of the grey circles? I have not made any progress so far.
1
vote
0answers
23 views

Cartesian to geodetic conversion of 3D bounding box - How to calculate latitude and longitude from an axis aligned bounding box

I have a geometry with its vertices in cartesian coordinates. These cartesian coordinates are the ECEF(Earth centred earth fixed) coordinates. This geometry is actually present on an ellipsoidal model ...
0
votes
2answers
66 views

Pentagon with two right angles (aka Van Aubel's Theorem)

My problem is the following: given that $ABCDE$ is a convex pentagon such that $AB=BC$, $CD=DE$, $M$ is middle point of side $EA$ and the angles $\widehat{ABC}=\widehat{CDE}=90°$, find the measure of ...
1
vote
1answer
39 views

Calculate PQ if AC = 20

I need to calculate PQ knowing that AC = 20. This is what I got so far: If I call the point between P and A, "M" and If I call the angle: $$\measuredangle{QPB} = y$$ Then: ...
0
votes
2answers
23 views

Find the geometric locus of vertices A of the triangles ABC with the given base BC and such that $\widehat{B} > \widehat{C}$

When I tried it, I figure that the right triangle, with angle A being 90, to satisfy the question. I just don't think is quite correct. Any suggestions?
0
votes
1answer
18 views

$P$ is a point on a hyperbola whose focal points are $F_1$ and $F_2$. $Q$ on the line that bisects $\angle F_1PF_2$. Prove $|PF_1-PF_2|>|QF_1-QF_2|$.

$\require{cancel}$ Sorry for the grammatical mistake in the title; it was needed to keep the title under 150 characters. $P$ is a point on a hyperbola whose focal points are $F_1$ and $F_2$. $Q$ is ...
3
votes
1answer
88 views

Ellipse like on sphere

Find the locus of all points on a sphere such that the sum of geodesic distances from two fixed points F1 and F2 on it is a constant, less than its diameter. ( When radius of sphere goes to infinity, ...
2
votes
1answer
55 views

Is it possible to accurately calculate an irregularly shaped frustum's volume?

I have the following water basin Now imagine this basin is filled with water to the top, is there anyway to accurately calculate the volume of water stored in it using only top and bottom areas A1 ...