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

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2
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0answers
33 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 ...
7
votes
0answers
34 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
20 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
22 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
18 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 ...
1
vote
0answers
15 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
38 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
2answers
29 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
15 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 ...
2
votes
1answer
40 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
27 views

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

$PQRS$ is a trapezium, with $PQ$ parallel to $RS$. $PQ = 20$ cm, $RS = 3$ cm, $PQR = 300$ cm and $QPS = 600$ cm. What is the length of the line joining the mid–points of $PQ$ and $RS$?
1
vote
2answers
38 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? ...
-3
votes
1answer
41 views

Lines through vertices of regular hexagon and regular pentagon [on hold]

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
69 views

Imaginary curvature. [on hold]

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
30 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
33 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
25 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
22 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
16 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
14 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
31 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
59 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
17 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 ...
33
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
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0answers
18 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
60 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
34 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
20 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
16 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 ...
2
votes
1answer
42 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
47 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 ...
1
vote
2answers
145 views

Is there any reason why $4-\pi$ is quite close to $\frac{\sqrt{3}}{2}$?

In this question obviously the error of our "approximation" is $4-\pi=0.858...$ . I tried to reconstruct the false argument with $\tau=2\pi$, and the error in that case would be $8-\tau=1.716...$, ...
0
votes
1answer
24 views

Euclidean and rectilinear distance and nonlinearity

Can some one please explain why Euclidean distance and rectilinear distance make a problem nonlinear? Thanks
2
votes
0answers
41 views

Realisations of associahedra

I seem to have lost the reference to a realisation I am interested in. Hopefully someone can steer me to a paper that fully explains the realisation. For the case $K_2$(the 5-gon) the following ...
2
votes
1answer
24 views

Is it possible to create a pop-up figure that yields a truncated cone?

Problem I have a geometrical problem. Consider the cone in the figure below. Is it possible to create a two-dimensional shape that extends to the three dimensional truncated cone? The idea is to fold ...
0
votes
1answer
26 views

What is the hyperbolic plane equivalent to translation in euclidean space

in euclidean plane one can move polygons like rectangles, triangles etc. around by isometries, e.g. translations. For instance if we consider a rectangle with midpoint $0\in\mathbb{R}²$ then the image ...
2
votes
1answer
44 views

Application of Bessel Function

I have read number of books and online literature on Bessel function. Theoretically, I have known about Bessel function. What is practical significance of Bessel function? How can Bessel function ...
0
votes
1answer
33 views

Geometry cube problems [on hold]

We form four identical numbered cubes using the net shown. Like $$ \begin{matrix}&&1&\\3&6&5&4\\&&2&\end{matrix} $$ Then glues them together to form a 2*2*1 ...
0
votes
0answers
18 views

Intuitive affirmation on convex sets

Let $D_1, D_2$ two open, bounded and convex domain in $R^n$. Suppose that $D_2 \supset \overline{D_1}$, and the boundaries of these sets are of class $C^1$. Fix $x \in \partial D_1$ and suppose that ...
0
votes
0answers
19 views

Strain mapping spherie to plane [on hold]

How should the coefficients E, F and G for latitudes/longitudes of a unit sphere metric be operated upon in a transformation representing surface parameter straining to map the spherical surface to a ...
0
votes
0answers
14 views

Calculate new geo coordinate from another using a distance and degrees

I'm trying to calculate a new point based on another point, distance (miles) and magnetic direction from the original point. Say I had a point ...
1
vote
1answer
37 views

Prove In Equilateral Triangle $ABC$ $AM$ and $AN$ are equal

$ABC$ is a equilateral triangle.Line $xy$ passes through vertex $A$ (but doesn't intersect any sides of triangle).$H$ is a point on Line $xy$ which angle bisector of $HAB$ and exterior angle of $B$ ...
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votes
1answer
51 views

Polar Coordinate usind De Moivre’s Theorem

I need the solutions for the following problem: Find all solutions over $\mathbb{C}$ to the equation $x^3=i^2$. I tried using De Moivre’s Theorem can't get around it. Note: The question originally ...
43
votes
4answers
5k views

How far can one see over the ocean?

Since Earth is a sphere, one has only a limited visibility radius. How far is that, actually? This Q&A was inspired by this question, about whether or not Legolas can see the 24km distant Riders ...
-2
votes
0answers
43 views

Euclidean Geometry of a triangle [on hold]

Let p and q be radii of two circles through A, touching BC at B and C respectively. Then prove that pq = $R^2$ . Actually I got this in book and there also it was not clearly mentioned about about R ...
-2
votes
0answers
58 views

Euclidean Geometry [on hold]

Let $ABC$ and $A'B'C'$ be two non-congruent triangles whose sides are respectively parallel . Then prove that $AA',\, BB', \, CC'$ (extended) are concurrent. Look I came across this problem in a ...
6
votes
1answer
53 views

prove equilateral triangle

Recently I have encountered such a proving problem. As shown below, given a triangle ABC, AD intersects BC at D so that AD is perpendicular with BC, BE intersects AC at E so that BE is the angle ...
7
votes
1answer
71 views

Direct formula for area of a triangle formed by three lines, given their equations in the cartesian plane.

I read this formula in some book but it didn't provide a proof so I thought someone on this website could figure it out. What it says is: If we consider 3 non-concurrent, non parallel lines ...
0
votes
1answer
22 views

Latitude and longitude to screen coordinates using “mapping points”?

I wrote a simple application which has a static image. I have 2 types coordinates for a point (or points if it is necessary): latitude and longitude; x and y for a screen. So I can get some ...
0
votes
2answers
36 views

Area such that $d(P, AB) \leq \min \{d(P,BC), \ d(P,AC)\}$

$d(P,L)$ means distance of point $P$ from line $L$. There are three points $A(4,4)$, $B(8,4)$ and $C(4,6)$. We need to find the area of the region satisfying $d(P,AB) \leq \min \{d(P,BC), ...