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

7
votes
12answers
962 views
+50

Irrational numbers in reality

I have a square stone slab 1 metre by 1 metre, by the Pythagorean identity the diagonal from one corner to another is given by $\sqrt 2$. However $\sqrt 2$ is an irrational number, could someone ...
-3
votes
0answers
12 views

Formula to calculate angle on a fan or semicircle [on hold]

strong text![FAN][1] [1]: http://i.stack.imgur.com/upD4W.pngstrong text How do I calculate the angle shown in the picture given the height, width, and the arc deduction of 2? I had applied the ...
3
votes
2answers
61 views

Volume of a sphere with two cylindrical holes.

Consider a sphere of radius $a$ with 2 cylindrical holes of radius $b<a$ drilled such that both pass through the center of the sphere and are orthogonal to one another. What is the volume of the ...
2
votes
2answers
421 views

Given a fixed perimeter, which shape will have the maximum area?

I think the answer is a circle. If so, then what is the rigorous prove?
0
votes
1answer
16 views

Line between points in projective space?

I am trying to find the line through the points $(0 : 1 : 0)$ and $(1 : 1 : 1)$ in $\mathbb P^2$ and $(0 :1 : 0: 1)$ and $(1: 1: 1: 0)$ in $\mathbb P^3.$ Would the first line be the set of points ...
0
votes
0answers
12 views

Questions on curvilinear asymptotes

I just saw curvilinear asymptote which sort of fascinated me. A little bit of thinking raised two questions for which I couldn't get the the answer by googling. Is there a general method to find a ...
0
votes
0answers
7 views

Showing there is a cartesian coordinate system on EG.

I'm pretty sure I should just show there is a bijection between the points in EG and elements of R^2. How do I do this? note: EG=Euclidean Geometry
7
votes
0answers
42 views

Can ${n \choose 2}$ points be covered by lines determined by $n$ points?

Let $S=\{(a_1,b_1),\ldots,(a_{n \choose 2},b_{n \choose 2})\}$ be ${n \choose 2}$ points on the plane. Does there exist $n$ points, such that the lines determined by the $n$ points cover all the ...
0
votes
1answer
11 views

find a point such that the distance between this point and a plane is equal to the distance between another point and a line

I have: $r:(2,1,0)+\lambda(0,4,-3) \qquad \pi:4y-3z-4=0 \qquad A=(2,4,4)$. I have to find a point $C$ such that $d(C,\pi)=d(A,r)$ where $d$ is the distance
5
votes
3answers
10k views

How to determine the arc length of ellipse?

I want to determine the arc length of a ellipse. So what data should I know ? And what law should I use ? For example I have this ellipse on picture below: How can I determine the $d$ length of ...
0
votes
0answers
5 views

Can Magnification/Scaling (transformation) be prepresented by a vector?

Vectors represent three bits of information: Magnitude, Line of Action, and Direction. A Translation (transformation) can be represented by a vector: object is moved By so much (magnitude) Along a ...
0
votes
0answers
7 views

Parametric equations for hypocycloid and epicycloid

Suppose that the small circle rolls inside the larger circle and that the point $P$ we follow lies on the circumference of the small circle. If the initial configuration is such that $P$ is at ...
2
votes
2answers
31 views

When the intersection between a sphere and a cylinder is planar?

We have a sphere and a circular cylinder. Let the sphere center be $O$ and radius $R$, and the cylinder axis $a$ and radius $r$. I solved the specific case intersection graphically on 2 planar ...
1
vote
0answers
11 views

For each point on a line there exists a unique perpendicular line through that point

I'm trying to show that in an absolute plane (only the first four axioms without the parallel axiom hold) for each Point $P\in l$ there exists exactly one perpendicular line through $P$. My idea was ...
3
votes
1answer
345 views

How many points does 'the-most-point-contained-circle' contain at least?

Question : Letting $n\ge 2\in\mathbb N$, how can we find $f(n)$ such that the following two propositions are true? If finding $f(n)$ is difficult, then how can we find 'good' function $g(n),h(n)$ ...
14
votes
3answers
364 views

How did Beltrami show the consistency of hyperbolic geometry in his 1868 papers?

This is in response to comments and the answer by user studiosus to this question: As for Beltrami's work: Consistency of a geometry from (post) Hilbert viewpoint has nothing to do with ...
2
votes
1answer
9 views

Given a number of vertices , a radius, and rotation calculate vertices' coordinates for regular polygons

So, I know half the answer to this but I don't know how to adjust it for rotation. I believe formula the below is correct if I did not have to take into account rotation. $r \cos(2 \pi i / n) = y$ ...
0
votes
0answers
11 views

Point on ellipse after walking a distance on the perimeter [duplicate]

I've the equation of an ellipse. Given a point (x,y) on the ellipse and a length L , I want to find the coordinates (x1,y1) of the point where I'd end up after taking a walk of length L from (x,y), ...
3
votes
1answer
40 views

Average distance to a random point in a rectangle from an arbitrary point

I'm interested in the mean distance between an arbitrary 2D point, $(p, q)$, and a uniformly distributed point inside a rectangle defined by the lower left and upper right vertices $(x_0, y_0)$ and ...
1
vote
0answers
15 views

Find Formal Proof on Loci Theorems

Please help me to prove this theorems of loci Theorem 12 The locus of a point at a given distance from a given line is two lines parallel to the given line and at the given distance from it. Theorem ...
1
vote
2answers
43 views

If a curve $\gamma$ through two points $P,Q$ satisfy $\|Q-P\| = \int^{t_1}_{t_0} \| \gamma^{'} \| \, \text {d}t$, then $\gamma$ is a straight line?

In a theorem called "A straight line is the shortest curve through two given points", I prove that for any two points $P,Q \in \mathbb R^2$ and any curve $\gamma : (a,b) \rightarrow \mathbb R^2$ with ...
0
votes
0answers
7 views

$\frac{4}{3}(1,-1,0)^T+\textrm{vect} \left((-1,1,-1)^T\right)$

Here I have a passage on the conclusion, but I do not understand it. the conclusion say : $f$ is the oriented axis of screw.. how I can from $\frac{4}{3} \begin{pmatrix}1\\1\\0 ...
6
votes
2answers
45 views

Counter example to Mostow's rigidity theorem for 2-manifolds.

I am trying to understand a counter-example to Mostow's rigidity theorem. Here is the counter example I want to understand. Take two non-isometric octagons with the sum of interior angles equal to ...
1
vote
1answer
293 views

Claim: Equilateral triangle is intersection of three equal circles while $R\rightarrow \infty $

I believe that equilateral triangle is intersection region of three equal circles with radius $R\rightarrow \infty $ , which have the same specific distance to each other. While distances changes ...
3
votes
2answers
289 views

Axis aligned rectangle inscribed in rotated rectangle

I start with an axis aligned rectangle, $R$, that I rotate by the angle $\theta$ to get $R'$. Afterwards I'd like to identify another axis aligned rectangle, $P$ with the following additional ...
1
vote
1answer
5k views

How do I find the base angles without a vertex angle in a isosceles triangle?

How can I find the base angles in a isosceles triangle if the vertex angle is missing? Normally, I would go: 2x + vertex angle = 180, but now even the vertex is missing, the only thing I have is a ...
5
votes
1answer
547 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 ...
5
votes
1answer
474 views

Space-filling polyhedra (or honeycomb) survey?

Is there a survey anywhere of space-filling polyhedra? MathWorld's article, space-filling polyhedron, mentions about 400 being seen in pre-1981 books and papers. Wikipedia mentions 28 convex uniform ...
1
vote
0answers
8 views

union of two Geodesics

Let $X$ be a metric space. $a,b,c \in X$ and $\sigma_1 , \sigma_2$ geodesics from $a$ to $b$. Let $\sigma$ geodesic from $b$ to $c$. Want to show : $\sigma_1 \cup \sigma $ geodesic $\Rightarrow ...
0
votes
1answer
17 views

Length of tendon in circle [on hold]

What is the length of chord that pass on two specific point. For example I have circle ( r=1) point1 :(x1,y1) point2(x2,y2); length of chord?
2
votes
1answer
614 views

Intersection of Two Circles

I have two circles as: $C_1: (x-x_1)^2+(y-y_1)^2=r_1^2$ and $C_2: (x-x_2)^2+(y-y_2)^2 =r_2^2$ and these circles have non-empty intersection. In other words $\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\leq ...
23
votes
2answers
498 views

What is the Coxeter diagram for?

I understand that Coxeter diagrams are supposed to communicate something about the structure of symmetry groups of polyhedra, but I am baffled about what that something is, or why the Coxeter ...
2
votes
1answer
61 views

Calculationg the angle of a triangle

I am trying to find a specified angle of a triangle. In triangle $ABC$, $\angle A = 20^\circ$. $D$ and $E$ are points on $AB$ and $AC$, where $AB=AC$. $\angle EBC = 50^\circ$ and $\angle DCB = ...
3
votes
2answers
49 views

Prove that the circle which contains ATB and incircle of ABC touch in one point(T).

Incircle of $ABC$ touches $AC$ in $D$, $BC$ in $E$ and $AB$ in $K$. $J$ is the center of the excircle which touches the side $AB$. The circumcircle of $ADJ$ and $BEJ$ intersect in point $J$ and $T$. ...
10
votes
2answers
117 views
+100

Geometric Interpretation of the Cross-Ratio

The cross ratio of 4 points $A,B,C,D$ in the plane is defined by $$(A,B,C,D) = \frac{AC}{AD} \frac{BD}{BC}$$ And it's a ratio which is preserved under projections, inversions and in general, by ...
0
votes
0answers
19 views

a question about differential geometry, the relation between osculating plane and the points of $\alpha(s)$

question:please prove the limit position of the circle passing through $\alpha(s)$,$\alpha(s+h_{1})$,$\alpha(s+h_{2})$ when $h_{1}$ and $h_{2}$ approaches 0 is a circle in the osculating plane at s, ...
0
votes
1answer
28 views

Trying to define a simple “warp” function

I'm trying to define a 2D "warp" function y=f(x,w). A picture is worth a thousand bytes: I am looking for a simple function f(x, w) that satisfies the ...
13
votes
8answers
6k views

Why Circle encloses largest Area?

In this wikipedia, article http://en.wikipedia.org/wiki/Circle#Area_enclosed its stated that the circle is the closed curve which has the maximum area for a given arc length. First, of all i would ...
0
votes
0answers
13 views

Is kahler geometry related to finsler geometry? [on hold]

Is kahler geometry related to finsler geometry? Is the metric $\partial_a\phi\partial_b\phi$ always kahler?
1
vote
1answer
28 views

Finding the length of $BC$ in a quadrilateral

Calculate the length of $BC$. I first started by letting $M$ the point of intersection of $AC$ and $DB$. Now $MB^2+MA^2 = 9$, $MD^2+MA^2 = 16$, $MD^2+MC^2 = 36$. Therefore, $BM^2+MC^2 = BC^2$ Can ...
1
vote
2answers
14 views

Geometry: What is the height of a solid pyramid

So the question is OPQRS is a right pyramid whose base is a square of sides 12 cm each. Given that the the slant height of the pyramid is 15cm. And now I need to find the Height of the pyramid. I ...
0
votes
2answers
36 views

What does 'forms a right-handed set' mean?

In a question I am reading, the following question appears. What if $\vec{A},\vec{B}$, and $\vec{C}$ are mutually perpendicular and form a right-handed set? What exactly does "form a ...
-1
votes
3answers
37 views

point on a line and distance from a point [closed]

I have point(x1,y1) and point(x2,y2) these are end point of line and point(m,n) is a point. How can i find Point(a,b) which lies on the line ,that is the shortest path from point(m,n) to the line
-8
votes
0answers
58 views

Prove that.. Please quick. [on hold]

If the length of perpendicular from the point $(1,1)$ to the line $ax-by+c=0$ be $1$, show that $1/c+1/a-1/b=c/2ab$. if $p$ and $p'$ be the length of the perpendiculars from the origin upon the ...
2
votes
0answers
24 views

Unique perpendicular line

Consider an absolute plane (i.e. it satisfies all axioms except the parallel axiom). Let g be a straight line and P a point not in g. Then there is a unique straight line going through P which is ...
0
votes
1answer
13 views

Inscribed Rhombus

Can a rhombus that is NOT a square be inscribed in a circle? A quadrilaterals opposite angles must add up to 180 in order to be inscribed in a circle, but a rhombuses opposite angles are equal and do ...
0
votes
1answer
11 views

For which functions $r$ is the curve $r(t)(\cos t,\sin t)$ regular or unit speed?

Decide conditions on smooth function $r$ such that $\nu$ is a regular curve and decide functions $r$ for which $\nu$ has speed $1$. Let $r: \mathbb R \rightarrow \mathbb R$ be a smooth function ...
56
votes
1answer
3k views

About Euclid's Elements and modern video games

Update (6/19/2014) $\;$ Just wanted to say that this idea that I posted more than a year ago, has now become reality at: http://euclidthegame.com/ 12.292 users have played it in 96 different ...
1
vote
1answer
21 views

Prove that there is exactly one perpendicular line

Consider an absolute plane (i.e. it satisfies all axioms except the parallel axiom). Let $g$ be a straight line and $P$ a point not in $g$. Then there is a unique straight line going through $P$ which ...
4
votes
2answers
662 views

Resource for learning straightedge and compass constructions

Does anyone know a good resource for learning about straightedge and compass constructions besides "The Elements?" I tutor geometry to middle-schoolers and high-schoolers and thought that including ...