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

learn more… | top users | synonyms

0
votes
2answers
30 views

Locus of Point P

Consider a circle $\circ$ of diameter $AB$ and a constant point $C$ on $AB$. Consider also a random point $Q$ on $\circ$. On $QC$ (but outside of those two points) we take a point $P$ such that ...
0
votes
1answer
22 views

Edge length of a Dodecahedron

Good morning, If I have a 12 sided regular pentagonal structure (Dodecahedron) and the widest point has 3.5m diameter, what is the length of an edge (if they are all the same). Regards, Connor
2
votes
0answers
38 views

Uniqueness of projective plane of order 5

Is there a slick way to see the uniqueness of projective plane (equivalently, an affine plane) of order $5$?
1
vote
1answer
30 views

Find out the $\angle PRQ$

please, help me to solve this.How can I proceed.I just need help. $PQR$ is a triangle. $M$ is a point on $QR$.here,$QM=1/3RM$ , $\angle RPM=30^ \circ$ and $ \angle QPM=20^ \circ$ now,$ \angle PRQ=??$ ...
2
votes
2answers
46 views

Volume of a parallelpiped from its sides and diagonals?

If a parallelogram has sides of length $a$ and $b$, and diagonals of length $d$ and $e$, then we can find its area in the following way. By the polarization identity, we have $a b \cos\theta = ...
0
votes
1answer
27 views

Angle of a cube's diagonal to one of its sides.

In $\mathbb{R}^n$, let $\theta$ be the angle between one of the $n$-cube's edges and its longest space diagonal. What is the measure of $\theta$ as $n$ goes to infinity? My thoughts lead me to ...
0
votes
0answers
6 views

Determining the minimal number of axis to test against in the SAT (Separating Axis Theorem)

Most implementations of the SAT algorithm I've seen involve testing each axis in either shape being tested against for collisions. But I recently implemented the SAT algorithm in python and noticed ...
0
votes
0answers
39 views
0
votes
1answer
29 views

A circle with radius $r$ has $k$ points within its radius. What is the min number of points a square with side $2r$ need to maintain this?

Consider that I have a circumference $c$ with radius $r$ that has $k$ points within its distance. As shown by the following graphic: For perfomance issues, I need to normalize this circumference ...
2
votes
1answer
17 views

Find the area of the minor segment.

Find the area of a minor segment formed by a circle of radius $6 cm$ and a chord whose distance from the centre of the circle is $3cm$. I tried it in this way: So i tried finding out $\theta$ which ...
1
vote
1answer
22 views

need explanation of what exactly is a directrix & focus?

((I'm not asking why do we need to know conic sections etc.) Like other similar questions.) I actually love math & currently learning conic sections in class, neither my textbook or teacher ...
1
vote
1answer
35 views

Four Square and Eight Promblem

Please help-this problem is pretty difficult for me for some reason.
1
vote
2answers
27 views

Geometry Right triangles in a rectangle, find the area.

Please help, I've been struggling to figure out this problem for too long... Given the area of rectangle $ABCD = 1200 \text{ unit}^2$, find the area of right triangle $ABE$
1
vote
1answer
28 views

Finding angle in isosceles triangle

An isosceles triangle ABC have AB=AC. Angle A measures 20. On AC, point E is such that AE=BC. Find measure of angle BEC without using trigonometry.
1
vote
1answer
16 views

From world space to object's space. Scaling.

I am developing a ray tracer and I need to compute intersections between many surfaces and rays. A classical method to make the computation time lower and the code simpler is to define some constants ...
7
votes
2answers
80 views

Calculating Angles at Vertices

This is quite a tricky question and I can't answer it.
1
vote
2answers
29 views

Geometrical place with circles…

How to find the geometrical place of all centers of a circles that tangent from inside to the circle $x^2+y^2=R^2$ and the $y$-axis? (Suppose that $x,y\geq 0$)
4
votes
1answer
37 views

Is my proof correct? The group of rigid motions of the cube is $\cong S_4$.

I want to solve the following exercise from Dummit & Foote. My attempt is down below. Is it correct? Thanks! Show that the group of rigid motions of a cube is isomorphic to $S_4$. My ...
-1
votes
0answers
31 views

Finding out the triangle numbers [on hold]

How will I find the number of errors without counting the triangle??? DO i have to find out the points and then permutations?
1
vote
2answers
21 views

Multiply segment

Suppose that I have the segment between the points (2, 2) and (3, 4). Empirically, drawing on a piece of paper, I can say that "doubling" the segment leads me to the segment (2, 2), (4, 6) and making ...
1
vote
2answers
33 views

Maximize the inradius given the base and the area of the triangle

BdMO 2013 Secondary: A triangle has base of length 8 and area 12. What is the radius of the largest circle that can be inscribed in this triangle? Let $A,r,s$ denote the area,inradius and ...
1
vote
1answer
37 views

Relationship between side length and circumradius of a regular convex polygon

I am trying to solve a programming challange on reddit and I want to understand how circumradius of a regular convex polygon relates to the side length. I've found that polygons can be separated into ...
0
votes
0answers
20 views

question about regular surface [closed]

Prove that set $s=\{(x,y,z):z^2+x^2+y^2=25\ \ and\ \ \ y>3\}$ is regular surface by using the definition of regular surface in book Manfredo Do Carmo
0
votes
0answers
17 views

Find the normal of a polygon with vertices that are not linearly independent in 3d

For example, take the vectors: $(1,2,3) (4,5,6) (7,8,9) (10,11,12) (13,14,15)$ What would the normal to the polygon be? I'm guessing it would be $(0,0,0)$? For vertices that are linearly ...
1
vote
3answers
159 views

“World's Hardest Easy Geometry Problem”

This question is a "corollary" (if you will) to the World's Hardest Easy Geometry Problem (external website). Formally, this is called Langley's Problem. The objective of that problem was to solve for ...
2
votes
1answer
27 views

Volume of spheres inscribed in a cone.

There are five perfectly spherical scoops of ice cream with various radii placed inside a waffle cone. Each scoop of ice cream is in contact with the adjacent scoop of ice cream. Also, each scoop ...
24
votes
3answers
325 views

Are there surfaces with more than two sides?

I'm watching a naive introduction to the Möbius band, the lecturer asks if it's possible to construct a one sided surface and then she says that there is one of these surfaces, namely the Möbius band. ...
0
votes
0answers
22 views

Finding midpoint of a cluster of points (2D)

Probably the dumbest question of the day, but given a cluster of points on a 2D graph, to find the "average" coordinate that sits at the midpoint of the cluster, is it as simple as averaging each ...
10
votes
3answers
209 views

Elementary proof that there is no paradoxical decomposition using triangular pieces

I am teaching a geometry course and I am trying to understand two definitions in the textbook ("Geometry with Geometry Explorer" by Michael Hvidsten.) Definition: The area of a rectangle is its base ...
1
vote
1answer
18 views

How to mesure lengths and areas in other euclidean, spherical and hyperbolic geometry?

I am learning how to measure lengths an areas in euclidean, spherical and hyperbolic geometry, but I'm getting very confused. First of all, I am told a rectifiable curve $\gamma$ has length defined ...
1
vote
3answers
63 views

Is convex hull of a finite set of points in $\mathbb R^2$ closed?

Is the convex hull of a finite set of points in $\mathbb R^2$ closed? Intuitively, yes. But not sure how to show that. Thanks!
3
votes
4answers
45 views

How do i prove this set has at most 2 elements?

Let $w,\alpha\in\mathbb{C}$ and $\delta,\epsilon >0$ such that $(w,\delta)\neq (\alpha,\epsilon)$ Define $G=\{z\in\mathbb{C} : |z-\alpha|=\epsilon \text{ and } |z-w|=\delta\}$ How do i prove that ...
2
votes
2answers
37 views

Orthogonal tangents to an ellipse

This is the problem I found back in the first year in the university. Suppose we have a non-degenerate (i.e. not a point and not an empty set) ellipse $E\subset \Bbb R^2$. Now define a set $D$ by a ...
0
votes
1answer
30 views

What is the radius of the spheres if all touch eachother?

A sphere of radius 1 is surrounded by 12 spheres of radius 1. But a small gap is left. What is the radius of the upper layer spheres if all the 12 kiss eachother so that no gap left? I mean particular ...
2
votes
2answers
31 views

area of ​​a quadrilateral

Get the area of ​​a quadrilateral? $‎\angle ‎A‎‎‎_{1}‎+‎\angle ‎C‎_{3}‎=30‎^{‎\circ‎}‎‎‎‎‎$‎ $\angle ‎A‎‎‎_{2}‎+‎\angle ‎C‎_{4}‎=90‎^{‎\circ‎}‎‎‎$ $CD=9, DA=5, BC=8 , AB=4$
0
votes
1answer
35 views

Why is this a line equation?

Define $$L=\{z\in\mathbb{C} : cz + \overline{cz} + w = 0\}$$ Where $c$ is a nonzero constant. How does $L$ represent a line?
0
votes
0answers
27 views

Equal area & perimeter [duplicate]

Find all triangles of which perimeter and area are equal. I have got answer for right angle triangles and equilateral triangles.
1
vote
4answers
47 views

Equal perimeter and area

Find all triangles of which perimeter and area are numerically equal. I have got solution for right angle triangles but not of others
0
votes
3answers
31 views

Sketching coordinates of C when it meets the x and y axis

The question: Curve $C$ has the equation $y=(x-k)^2 (x-k+2)$ Where $k$ is a constant and $k > 2$. Sketch $C$, showing the coordinates of the point where $C$ meets the $x$ and $y$ axes. I am ...
0
votes
4answers
53 views

Mathematics based on triangles

How to find the third cordinate of a triangle , where as other two points are known. and a angle is known. Lets say , the two points are (0,0) , (600,0) and we need to find the third cordinate . ...
0
votes
1answer
48 views

How find this this distance $d_{1}d_{2}=b^2$

On the plane we have two points $A(\sqrt{a^2-b^2},0),B(-\sqrt{a^2-b^2},0)$ with $a>b>0$ and the line $L$, of which the equation is given ...
3
votes
1answer
132 views
+50

How prove this result $\frac{x}{y}=\sqrt{\frac{\sqrt{5}+1}{2}}$

A tetrahedron $A-BCD$ is such all four faces are similar right triangle. and we let $$AB=a,BC=b,AC=c,AD=d,BD=e,CD=f$$ define $$x=\max{(a,b,c,d,e,f)},y=\min{(a,b,c,d,e,f)}$$ show that: ...
1
vote
0answers
31 views

Shifting a plot in polar coordinates

Say we have the plot of a function $r=f(\theta)$ and want to "relocate" it to $(h,k)$. Is there a general procedure for this? I have tried the following tactic to no avail on the following example: ...
0
votes
0answers
16 views

How to Generate a skewed Pyramid in MuPAD? [closed]

I would like to plot a skewed pyramid in MuPAD. I would like it to have a square base with side length 1. This would sit along the xy plane (centered at $(1/2,1/2,0)$). I want the vertex at ...
3
votes
1answer
52 views

Locus of the centres of equilateral triangles (contest problem)

Given a triangle $A_0A_1A_2$ determine the locus of the centres of the equilateral triangles $X_0X_1X_2$ satisfying the condition that each of the lines $X_kX_{k+1}$, $k=0,1,2$ passes through ...
2
votes
0answers
15 views

Can a cube always be fitted into the projection of a cube?

If we project the unit cube in $\mathbb{R}^n$ onto a $k$-dimensional subspace of $\mathbb{R}^n$ which contains the origin, can we always fit a $k$-dimensional cube of side length 1 into the ...
2
votes
3answers
52 views

Equation of a torus

First I am a newbie in maths so please forgive me if I am not as rigorous as you would like, but do not hesitate to correct me. I want to find the equation of a torus (I mean the process, not just ...
0
votes
3answers
28 views

Circumcircles of a trapezoid

I was just wondering, what types of trapezoids have circumcircles? I know one of them might be isoceles trapezoids, but are there any others?
1
vote
1answer
25 views

Is there another way to solve the value field of a parameter of an line.

Assume $P$ is a point in line $x+y=m$, where $m \in \Bbb{R}$. There are two points $A,B$ in circle $$x^2+y^2 = 10$$ such that $PA$ and $PB$ are tangent lines of the above circle. If line: $x+y=m$ has ...
2
votes
1answer
56 views

Incidence Geometry Proof

How do I show that the axioms of incidence geometry follow as theorems from the following axioms. 1) There exist exactly four lines. 2) Any two distinct lines are incident with exactly one point. ...