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

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4
votes
0answers
28 views

How many integer-sided right triangles are there whose sides are combinations?

How many integer-sided right triangles exist whose sides are combinations of the form $\displaystyle \binom{x}{2},\displaystyle \binom{y}{2},\displaystyle \binom{z}{2}$ for $x,y \geq 2$? Attempt: ...
0
votes
1answer
13 views

doing a math project my slopes don't make sense

I'm doing a project using slopes. I have a track and have released a marble at 3 different intervals on the track. I have 3 rises and 3 runs. They go from larger numbers (rise 58, 55, 49 to run 62, ...
0
votes
0answers
9 views

Berry's curvature equation

The following textbook Heisenberg's Quantum Mechanics shows an example of calculating Berry's curvature (top page on pg 518). It led to a following equation [1] $$ V_{m} = {- 1 \over B^2 } * i * ...
1
vote
1answer
16 views

Metric Spaces Whose Diameter is Achieved at Every Point.

Suppose $(X,d)$ is a metric space with diameter $\sup \{ d(x,y) \colon x,y \in X\}=1$. Call the point $x \in X$ an edge point to mean that $d(x,y)=1$ for some $y \in X$. Call the metric space ...
0
votes
0answers
17 views

Let D denote a point on base AB, and let E denote a point on leg BC of an isosceles triangle ABC.

The triangles ABC, CDE, and BDE are all isosceles, and triangle BDE is similar to triangle ABC. Determine the angles of each triangle. Since ABC and BDE triangles are similar, their angles have to be ...
2
votes
3answers
79 views

Is there a geometric meaning associated with the condition “dot product equals $1$?”

Consider $x,y \in \mathbb{R}^n$. Then the condition $x \bullet y = 0$ is easy to understand; it just means that $x$ and $y$ are orthogonal. Question. Does the condition $x \bullet y = 1$ have an ...
0
votes
1answer
18 views

Curve connecting two points in $\mathbb{R}^n$ passing through a hyperplane

Let $\pi$ and $\lambda$ be two distinct permutations of $1, 2, . . . , n$, and consider the points $p := (\pi(1),\pi(2), ... , \pi(n))$ and $r:= (\lambda(1), \lambda(2), ... , \lambda(n))$ in ...
0
votes
2answers
55 views

What is the perimeter of the rectangle formed by 7 separate squares with different sides? Explain how you arrived at your conclusion? [on hold]

Here is the the question: you have 7 squares with sides 1, 2, 2, 2, 3, 4, 5. These squares form a rectangle with no gaps or overlaps. What is the perimeter of the rectangle formed A) 34 ...
0
votes
0answers
8 views

Jumps in a flow to the outermost area enclosure of a surface

While studying some geometrical properties of some flows of surfaces, I encountered this problem: I consider some surfaces $E_t$ flowing to infinity. I also define $E'_t$ to be the outermost minimal ...
4
votes
2answers
30 views

Elementary 3D geometry

This is surely trivial, but my old brain can't remember how to do it. Assume a plane. A second plane intersects, forming line $AB$. The angle of intersection is $\theta$. A third plane intersects, ...
0
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0answers
14 views

Construction of the Area Function

I am following calculus by Tom M Apostol in which he has given the Axiomatic definition of the Area Function We assume there exists a class M of measurable sets in the plane and a set function a, ...
0
votes
0answers
13 views

Variant Lemoine's problem

You can see Lemoine's problem: Kiepert triangle: Let $ABC$ be a triangle, $BCA_0$, $CAB_0$, $ABC_0$ be three isosceles triangles constructed on the sides of $ABC$ with base angle $\alpha$. We called ...
-5
votes
1answer
52 views

Preplexity of Pi [on hold]

Why should we use the area of circle as $\pi$ multiplied by square of radius ? Can't we use another formula to get the specific answer? We know that $\pi$ does not equals to $\frac{22}{7}$ or ...
3
votes
3answers
53 views

Show that among all quadrilaterals of a given perimeter the square has the largest area

Show that among all quadrilaterals of a given perimeter the square has the largest area. By Ptolemy's theorem we have that if $a,b,c,d$ are the side lengths of the quadrilateral then $ac+bd \geq ...
0
votes
0answers
19 views

There exist cuspidal cubic sections in a nonsingular cubic surface in $\mathbb{P}^3$

This is part of Exercise 7.3 in Undergraduate Algebraic Geometry by Reid. Let $S: (f=0) \subset \mathbb{P}^3$ be a nonsingular cubic surface. For $P\in S$ prove that if $P$ is not on a line of $S$ ...
3
votes
1answer
35 views

Rotating a sphere

I'm trying to rotate a sphere, and I'm having a bit of a problem calculating the angle to rotate it by. I wonder if anyone can help me? On my sphere I've marked three points. If the centre of the ...
2
votes
0answers
15 views

Calculate the Angle between two vectors in 3d Spherical Coordinates

I have two vectors in spherical coordinates, both originating at the origin and both with the same magnitude equal to one. One is vertical: {1,0,0} and the other undefined: {Ms,Mt,Mp}. The other one ...
1
vote
0answers
34 views

what is relation between topology and geometry? [on hold]

what is relation between general topology and geometry ?( and example in this relation .) is there simple book in relation between general topology and geometry ?
0
votes
1answer
15 views

Length of one internal tangent with two external tangents

Two circles with radii 25 and 16 are tangent externally. The two common external tangents intersect the larger circle at A and B and the smaller circle at C and D. The common internal tangent ...
-5
votes
0answers
34 views

Find the volume of the following room [1] [on hold]

I was working on a project which required me to calculate the volume of the room. The picture of the room is given below: I tried splitting the shape across the diagonals but each time end up ...
0
votes
0answers
9 views

Mathematical theory for equally distributed dipole structures with inner equilibration

I'm looking for a mathematical theory for equally distributed dipole structures with inner equilibration. I know, that there exist two magnetic clusters, where the north and the south poles equally ...
0
votes
0answers
40 views

is the followng function $f$ surjective?

$f$ is a function mapping $x$ axis to plane $V$ defined by if $P(x,0)$ then $f(P) = (x,x^2)$ ? I am not so sure for my following answer : to show that $f$ is surjective, for every $A(x,x^2)$ there ...
-1
votes
0answers
17 views

Torus Cylinder intersection [on hold]

Two surfaces in 3D .. a Torus and a Cylinder with parametrizations respectively as: $$ \{ b + a \cos(u) ) \cos(v), (b + a \cos(u) \sin(v), a \sin(u )\}, $$ $$ \{a + b \cos(p), b \sin(p) ...
2
votes
0answers
33 views

what exactly is arc length element $ds$ or area element $dA$

I am reading a book on complex analysis and it has something like: The spherical arc length element on the Riemann sphere ($S^2$) works out to be $ds=\frac{|dz|}{1+|z|^2},$ and the spherical area ...
0
votes
1answer
12 views

3D Shape Name Recognition

I have 1: a right angled triangle, 2: an isosceles triangle, 3: a rectangle, 4: a parallelogram, and 5 a trapezium in the 2D picture which I am rotating about the red axis next to them. They produce ...
0
votes
1answer
47 views

How do I prove that sine is dependent only on the angle? [on hold]

I did the following: Taking one triangle and writing the pythagorean formula to it: $a^2+b^2=c^2$ and hence: $$\frac{o}{h}=\frac{\pm \sqrt{c^2-a^2}}{\pm \sqrt{a^2+b^2}}$$ I took another ...
0
votes
0answers
30 views

Given triangle w/ two congruent perpendicular bisectors, is it isosceles?

Given any triangle with two congruent perpendicular bisectors (the segment that is inside the triangle), must it be isosceles? Why? Trying to construct a non-isosceles one doesn't seem to work. I ...
4
votes
3answers
65 views

Are planes in $3$-dimensions two-dimensional?

Are planes in $3$-dimensions two-dimensional? The reason I ask is because mathematically the $xy$-plane exists in $3$D space but appears to be $2$D, but how can something $2$D be in $3$D space? I ...
1
vote
1answer
18 views

prove that $MN \parallel BC$ in an equilateral triangle

$\Delta ABC$ is equilateral with $M$ and $N$ being interior points. if $\angle MAB=\angle MBA=40^{\circ}$ $\angle NAB=20^{\circ}$ and $\angle NBA=30^{\circ}$. Prove that $MN \parallel BC$ from ...
0
votes
1answer
18 views

Conditions for convex hulls

What are the conditions for there to exist a convex hull on a set $X$ of points? I know that there exists a unique convex hull for a set of $X$ points, but must no $3$ points be collinear in ...
0
votes
1answer
34 views

How could I use the centroid and size of a triangle to find the coordinates of its vertices?

I'm making a 3D graphics program in OpenGL and I'm making a function to automatically place the centroid of a triangle on the specified xy coordinates. The triangle will be of a set size. Essentially ...
2
votes
1answer
26 views

Local isometry between simply connected manifolds

Suppose $D:\tilde{M}\rightarrow N$ is a local diffeomorphism between two simply connected smooth manifolds $\tilde{M}$ and $\tilde{N}$. $D$ is onto. In the case of $D$ being a covering map, it follows ...
0
votes
1answer
25 views

A proof in Desargues' geometry

The question is: Prove in Desargues' geometry that if a, b, c are three lines where a is parallel to both b and c then b and c intersect at the pole of a. Desargues' Geometry has the following ...
0
votes
2answers
52 views

minimising sum of distances

I have three points $A(-3.5, 0), B(2,0), C(0,3)$. I am looking for the fourth point $D(0,d)$ such that $AD + BD + CD$ is minimal. Fermat does not work here due to $D$ lying on the y-axis. I thought ...
0
votes
1answer
32 views

Centroid of heart shape

A heart shape is constructed using two identical circles with radius $r$. A line is drawn from point $T$ to $C$. There, two tangents are constructed, one to each circle, through $AC$ and $CB$. (The ...
0
votes
1answer
23 views

Size of a 3D object with relation to reference point [on hold]

I have a simple image of a table. I placed a reference ($10 \times 10$ rectangle) on top of it. I know the size of the rectangle and I want to calculate the size of the table. If I try simple ...
1
vote
3answers
40 views

The line $x+\sqrt{3} y-10=0$ makes an angle of $150$° with the positive sense of the $x$-axis. How can this be proven?

I cant figure out how this is correct. I know that $\tan(a)=m$ of a line but I cant figure this out. Could someone show how to prove the line makes an angle of $150$° with the positive $x$-axis? I ...
0
votes
0answers
22 views

tensor product of a line bundle with $\bigwedge^k T^*M$

I am reading a source that says: Let $L \to M$ be complex line bundle. Define $\Omega^k(M,L)=C^\infty(M,L \otimes\bigwedge^k T^*M)$. Can someone explain thoroughly what this means? What does it mean ...
0
votes
1answer
31 views

Equation of a curved line from a graph

I am trying to calculate an equation to represent the graph attached to this question. It's an extract from a take-off performance graph used in aviation. The second graph shows how it is used. The ...
1
vote
4answers
32 views

Problem based on circle geometry - related to circumcircles and angles finding the angles within a circle

Let the vertex of an angle $ABC$ be located outside a circle and let the sides of the angle intersect equal chords $AD$ and $CE$ with the circle. Prove that the angle $ABC$ is equal to the half the ...
0
votes
1answer
20 views

Convert quaternions to xyz degrees

I knew quaternion for the first time a few days ago and I still don't get the way it works even when reading explanations. All I want to do is to make a subtraction between two quaternions and convert ...
0
votes
1answer
21 views

Maximum hyperrectangle

Is there a way to determine the coordinates of the maximum hyper-rectangle in n-D space subject to linear constraints and $x_i\ge0$ ? Example: Argument Maximum of $x_1 x_2 x_3$ Given ...
0
votes
0answers
9 views

Faces of a Bipyramid over a a Simplicial Polytope

Is there a simple way of expressing the number of faces of a bipyramid built over a polytope that is known to be simplicial, using the number of faces of the original polytope? This seems an easy ...
1
vote
1answer
44 views

Proving the volume of sphere by using tiny volumes

How can I prove the volume of sphere, by using many cones starting at the center of the sphere? It doesn't have to be cones, pyramids also work.
0
votes
0answers
28 views

Describe curves by words

I am trying to describe the general aspect of the following curves My ideas: The curves are continuous, and defined for positive values of x, and giving negative values. Have logarithmic growth ...
-1
votes
1answer
24 views

Find the equation of locus of a point which is at a distance $5$ from $A$ $(4,-3)$ [on hold]

Find the equation of locus of a point which is at a distance $5$ from $A$ $(4,-3)$. Could some explain how to solve this in detailed.
1
vote
1answer
38 views

Two tangents BC and BD are drawn. Prove that Ob=2BC

Two tangent segments BC & BD are drawn to a circle with centre O such that $\angle$CBD=120$^{\circ}$. Prove that OB=2BC. What I've tried, BC=BD[two tangents drawn from a single point to the ...
-1
votes
3answers
57 views

Prove a geometry related equation.

$\Delta ABC$ is an isosceles triangle. $\angle BAC$ is an right angle. $BC$ is its hypotenuse and $P$ is any point on $BC$. Prove that, $PB^2+PC^2=2\times PA^2$. I have tried it in many ways and ...
0
votes
1answer
22 views

ABCD is a square of side 4cm. E is a point in the interior of the square such that CED is equilateral. Then find the area of ACE in sq.centimeters.

The given answer is $4*(\sqrt{3} - 1)$ I tried all the methods but could not match the answer. Please tell if the question is wrong. Thanks in advance.
0
votes
4answers
51 views

Move a dot along a path [on hold]

I have a multi-point, straight line path - to keep it simple it has three points, A B & C. A = 60,410 B = 127.5,410 C = 195,240 This is the 'template' path, I need to animate a dot moving ...