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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3answers
35 views

How do I find out whether three 3D vectors can form a right angled triangle?

I am asking this question for my son who is about finish the twelfth grade. I have already seen this question, however that did not actually answer my query. I have three vectors, \begin{align*} ...
1
vote
1answer
64 views

Intersection of a circle and a triangle

If we have a point $(0,6)$ which is the vertex of an equilateral triangle the distance of whose all vertices are equal from origin.Draw a circle of radius 3 centered at $(0,1)$.How many number of ...
2
votes
2answers
34 views

Determining hexes intersected by a line between two hexes on a hex grid

Given two hexes within a hex grid of tiles, is it possible to determine all the hexes which are intersected by a line draw from the centre of first hex to the centre of the second if you are only ...
2
votes
3answers
62 views

Decartes geometry: real numbers and the plane

In Decartes's geometry, we express every point in the plane (Euclidean goemetry) with a pair of real numbers, so we can transfer the geometry problem to algebra problem, but how can we know that the ...
2
votes
3answers
48 views

Euclidean “straight line” calculation

Please see image first.. I have as input the following (I presume these are in effect Euclidean coordinates): The angle and the length of the red line. The angle and the length of the green ...
2
votes
2answers
27 views

Calculate the closest point to the center of a circle from another circle on its radius.

There are 2 circles, the smaller one has its center on the bigger circles border, from that how can you calculate the coordinates the closest point on the smaller circle to the center of the bigger ...
4
votes
1answer
70 views

Determine these two angle (Isosceles triangle)

Please see the following diagram: This is an isosceles triangle. Let the angles be as follow: green = G, red = R, blue = B, purple = P G = pi - 2B Now my question is.. Based on the value of ...
1
vote
4answers
29 views

Find y-coordinate on a line between two (known) points

Iam a littlebit stuck with a simple task and hope to find some help here, since my days in school are now long time over and to be honest i can’t remember so well how to do it. I have a straight ...
1
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0answers
50 views

Congruent figures have equal areas. Why?

When we are first introduced to the idea of congruent polygons (generally triangles) in school, we often define congruent figures as "figures which have the same shape and size". However, today, ...
0
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0answers
28 views

Similar triangle, Quick question (Thick Lens Formula)

http://www.panohelp.com/thinlensformula.html On the right hand side, f is defined as focus of the lens, i understand why the image distance is (f + fm). However i have spent an afternoon and could ...
0
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2answers
19 views

Reflecting and Translating Points

Point R (-4,5) is reflected about the x-axis onto point R'. It is then reflected about the line y=-x to find R''. It is then translated using the vector <2,-2> to find R'''. Find R'''
1
vote
1answer
39 views

Converge of an inversion to a mirrorring

I want to ask something about a mirroring and a inversion in $\mathbb{R}^n$. An inversion in a sphere with center $m$ and radius $\rho$ can be written as $$ v \ \longmapsto \ ...
1
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1answer
39 views

Interactions between geometry and graph theory.

I'm looking for some nice theories or just exercises, with both geometrical aspects and graph theoretics aspects. Example may include for instance the 4-color theorem or Euler characteristics, maybe ...
0
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0answers
83 views

Trying to prove that two angles are congruent in a isosceles trapezoid

I was given this assignment to do the following. Write a paragraph proof for the following scenario. Given: KLMN is an isosceles trapezoid. Prove: ∠LKM is congruent to ∠MNL The thing is that I ...
0
votes
0answers
25 views

Metric for movement in 2D space

I have a set of points that represent the coordinates of an object moving in the 2D space at different points in time. Using this points I want to get a "measurement" that will describe the general ...
0
votes
1answer
19 views

show the equality of sections at right triangle

We have right triangle $ABC$ and squares $ABED$, $BCFG$ (see piture) lines $CD,AG$ intersects triangle sides at respectively points $H, I$ show that $HB=BI$ I tried to solve it looking for congruent ...
0
votes
0answers
35 views

proof of the existence of spherical sections of ellipsoids

i want to prove : Let L be proper ellipsoid with the origin as center in $E^{2m-1}$ .There exists a subspace $E^m$ such that $E^m$ intersects $L$ is an m-dimensional sphere it is proven by Dvoretzky ...
3
votes
5answers
70 views

The points $(0,0)$, $(a, 11)$, and $(b,37)$ are vertices of an equilateral triangle. Find the product $ab$.

"The points $(0,0),\;(a, 11), \text{ and } (b,37)$ are vertices of an equilateral triangle. Find the product $ab$." I'm not sure how to start this problem. I of course drew out an equilateral ...
1
vote
1answer
87 views

The square cover number and the number of horizontal sides

I am looking for a geometric upper bound on the square covering number of a rectilinear polygon. A square covering of a given polygon is a collection of squares, possibly overlapping, whose union ...
1
vote
1answer
140 views

Felix Klein's view on algebraic geometry

I think, as a first approach one would say that a geometry on a set $X$ is given by an inner product on $X$. Klein then links geometry to group theory by identifying a geometry on $X$ with a group of ...
0
votes
1answer
90 views

can anyone explain Pizza theorem?

This is the theorem : Theorem. If a circular pizza is cut into $4n$ slices by $2n$ concurrent cuts (which run right across the pizza) at equal angles to each other, and n people share the pizza by ...
0
votes
3answers
66 views

getting the slopes of the sides of an equilateral triangle given 2 points

I want to get the slopes of an equilateral triangle given the 2 vertices. Let's say they are (0, 0) and (5, 5). Graphing this would give 2 triangles forming a diamond. I tried to use distance formula ...
1
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3answers
18 views

Finding Angle Measures

An A-frame house is 40 feet high and 30 feet wide. Find the measure of the angle that the roof makes with the floor. Round to the nearest degree.
0
votes
1answer
32 views

What's the difference between these rotations?

1) Each point on the coordinate plane is rotated $\theta$ degrees about the origin. 2) Each point $P$ with the coordinates $(x,y)$ is rotated $\frac{\pi}{4}$ radians about the origin. The answer ...
0
votes
2answers
60 views

spherical triangle: law of sines

Given plane triangle ABC it is well known that the common value of the ratios appearing in the law of sines is equal to the diameter of the circle which passes through the three vertices. ...
1
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2answers
59 views

Describing all points 4000 miles from the north pole

I'd like to describe all of the points on the Earth's surface that are exactly 4000 miles from the North Pole. I know that this will eventually give me an equation for a circle; I want to find that ...
0
votes
0answers
36 views

Continuous, smooth derivative for two “stitched” ellipses

This is something of a whim, but it won't leave me. Consider two ellipses, P and Q, with $P(a<b)$, $Q(b<c)$ and $a<b<c$ (not $<<$). Is it possible that, by cutting P along its major ...
0
votes
2answers
40 views

How to find the third vertex of an isosceles triangle given 2 points.

This is the full problem: The points $A(5,1)$ and $B(-3,6)$ represent one of the equal sides of an isosceles triangle. Determine one of the possible points that would represent the third vertex of the ...
-2
votes
1answer
20 views

hard isosceles triangle/isosceles trapezoid question

Triangle ABC sits right on top of trapezoid DBCE. BC is parallel to DE. Triangle ABC's area is half of the area of trapezoid DBCE. What's the ratio of AC to AE?
2
votes
0answers
72 views

What if the cow could fly?

See grazing cow. Now keep the restriction that the length of the rope is $l\leq\pi r$ where $r$ is the radius of the barn, (I like to think of this as a goat tied to a silo) but now suppose the cow ...
1
vote
0answers
19 views

Is it possible to reconstruct a triangulation from its $1$-skeleton?

Let's restrict to triangulations $T$ of compact and closed smooth manifolds $M$ with $\dim M=2,3$. Such a triangulation is a PL manifold homeomorphic to $M$ which geometric realization is a simplicial ...
1
vote
2answers
42 views

Find the radius of four congruent circles inside a right triangle

Below is a homework assignment I'm working on, along with a correct method for solving it and what appears to be an incorrect method. I'm hoping someone could explain what is wrong with the second ...
0
votes
3answers
91 views

Area of the field that the cow can graze.

How do we find the area that the cow can graze? The question goes as follows-- There is a circular barn house surrounded by a huge grazing field. A cow is tied to the rope ($AB$) at the end $A$ as ...
0
votes
1answer
26 views

Why is it a borel set on the boundary of the unit ball of $E^n$?

Given $C$ convex body (compact convex set with non-empty interior points) in $E^n$ symmetric about the origin and containing the unit ball. Let $A(r)$ denote ,for every real $r >1$, the subset of ...
2
votes
1answer
107 views

Length minimizing curves are geodesic segments

I have a metric space $(X,d)$, a geodesic arc is defined to be a continuous function $\gamma : [a,b] \rightarrow X$, $a < b$, which is (globally) distance preserving and geodesic segments are ...
1
vote
1answer
36 views

what is the meaning of asphericity of convex set in a linear normed space?

I am trying to understand the definition of spherical to within $\epsilon$ for a convex body in a linear normed space, as given in Aryeh Dvoretzky's paper [1] (section 2, page 203): A convex set ...
1
vote
1answer
42 views

An angular inequality

In a triangle $ABC$, let $D$ and $E$ be the feet of the angle bisectors of angles $A$ and $B$, respectively. A rhombus is inscribed into the quadrilateral $AEDB$ (all vertices of the rhombus lie on ...
0
votes
3answers
36 views

Inscribe a rectangle inside an ellipse

A rectangle is to be inscribed inside a horizontal ellipse (whose major or minor axis is parallel to x axis). Is the horizontal orientation of the rectangle (two sides parallel to x axis) the only ...
0
votes
1answer
53 views

If you know 2 sides of the triangle, wha is the third side?

I understand why A & C are correct but I don't get how E is a possible length since whatever number I plug in for x I get a number greater than 5x+5...
-2
votes
1answer
45 views

SAT geometry and algebra [closed]

QI: Segment XY is the diameter of a circle. Point Z is placed on the circle such that the length of XZ is 6 and the length of ZY is 8. What is the area of the circle? (A) 10π (B) 25π (C) 36π (D) ...
0
votes
0answers
38 views

Generalizations of functions

I'm trying to collection examples of mathematical entities that are generalizations of functions. The use of the word "generalization" here doesn't need to be strict, as in every function is an $X$ ...
1
vote
0answers
39 views

Tangent bundle is orientable

I am having some trouble finishing a proof that the tangent bundle of any manifold is orientable. What I've done so far is calculate the transition function between two standard charts on the bundle. ...
2
votes
2answers
55 views

Primary school math regarding circles [closed]

----------//-----------------------------------__________ Please see the figure below the question is in the ...
2
votes
2answers
40 views

Finding a 3rd coordinate of the rectangle points in 3d

I have a 4 3-D-points, each of them has only 2 of 3 known coordinates, as follow (? is unknown here): P5 (P5x, P5y?, P5z) P6 (P6x, P6y?, P6z) P3 (P3x, P3y, P3z?) P4 (P4x, P4y, P4z?) They build ...
2
votes
3answers
63 views

Are there circles in $\mathbb{R}^d$ taking no rational values?

I recently stepped over a little detail in a thesis I still wonder about. If one looks at $\mathbb{Q}$, then it is dense in $\mathbb{R}$, and we have no problem finding real numbers that don't belong ...
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votes
3answers
25 views

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

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
2
votes
0answers
33 views

Packing circles in circle vs semicircle vs quarter of circle

Consider $N$ disjoint circles with radius $1$ packed into a larger circle $C$. Let $R$ be the smallest possible radius of $C$, allowing the best packing density. Now take the $N$ unitary circles ...
0
votes
3answers
35 views

For a line how to find $y=mx+c$ if $x_1,y_1$ and $x_2,y_2$ in hand

How can I find $y=mx+c$ for a line? I have only two end points $x_1,y_1$ and $x_2,y_2$.
0
votes
1answer
20 views

Find a projectivity to create a graph.

I have the tetrahedron {xyzt=0} in projective space with homogeneous coordinate (x,y,z,t). I need to create a graph but the tetrahedron in affine coordinate is {xyz=0} and I can't visualize the ...
0
votes
0answers
26 views

how to find the optimal path for a rescue robot?

The rescue robot is searching signals in a huge rectangle area without obstacles. We assume: - only one signal source in the area in a constant location. - the robot is small enough to be regard ...