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

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3
votes
1answer
42 views

Areas between intersecting chords

In the circle below let the two chords be called $C_1$ and $C_2$, and their intersection be some point that is not the center. The chord power theorem tell us that $a \cdot b = c \cdot d$. I am ...
1
vote
1answer
13 views

Right triangle inscribed in a circle with the equation of the circle is $r=2a\:cos\left(\theta \right)$

How to prove that the equation of the circle (the image given below) is $r=2a\:cos\left(\theta \right)$ using polar coordinates? Please anyone help me, I've been stuck in this problem for like 2 hours ...
1
vote
2answers
55 views

How is it called when one ellipse is “more elliptical” than another one?

Assume you have two ellipses, $A$ and $B$. Now $A$ looks "flatter" than $B$ because its ratio $\frac{\text{major axis}}{\text{minor axis}}$ is bigger. This means it "looks less" than a circle. How is ...
0
votes
0answers
19 views

reparametrized geodesics

I am doing this exercise : Let $X$ be a metric space. A continuous path $c : I → X$ is a linearly reparameterized geodesic if and only if $d(c(s), c(t)) = 2 d(c(s), c((s + t)/2))$ for all $s, t ∈ I$; ...
0
votes
3answers
43 views

Math homework, so much guessing work? [closed]

Riki hires a digger to load topsoil onto his trailer. The bottom of the trailer is square with sides 1.5 meters long. The height of the sides of the trailer is 25 centimeters. The digger shovel holds ...
12
votes
1answer
117 views

Koch snowflake versus $\pi=4$

The only proof I could find of the Koch snowflake having infinite perimeter was by calculating the perimeter $P_n$ after the $n$th iteration $$P_n = 3s\left(\frac{4}{3}\right)^n,$$ where $s$ is the ...
2
votes
1answer
17 views

Finding the polar line of the intersection of a polar line and a tangent

Let $K$ be an inversion circle with center $O$ and let $C$ be the point of intersection of two lines tangent to $K$ in $A$ and $B$. Then let $E$ be the intersection of the line $AB$ and the line ...
0
votes
2answers
33 views

How many milliliters to fill cone

A right circular cone has a depth of 103 mm and a top diameter of 82.4 mm. The cone contains water to a depth of 30.0 mm. How many more milliliters of liquid need to be added in order to fill the ...
0
votes
1answer
20 views

line segment intersection strange results

I'm using this formula. I am getting very strange results with (1,3) to (29,17) and (6,19) to (7,8). I got an X* value of 7. When I plugged this into my intercept calculator it said they intercept at ...
0
votes
2answers
36 views

Find side length of cube [closed]

The surface area of a cube is its volume multiplied by two. Find the side length of the cube (no units required) I have no idea where to start for this question, Can someone please help me?
1
vote
1answer
28 views

Find angle and hypotenuse of right angled triangle

Find the missing side and the hypotenuse of a right triangle that has a side length of 5 cm and a perimeter of 30 cm. I'm confused. Can somebody please explain to me how to do this step by step? Not ...
-4
votes
1answer
29 views

Pythagorean Theorem Statement True or False… [closed]

True or False The Pythagorean Theorem is: In a triangle having legs of length $a$ and $b$ and hypotenuse of length $c$, $a^2+b^2=c^2$
0
votes
0answers
17 views

Geometric properties invariant to perspective

Suppose you have a few random dots on a piece of paper. I need to find some property of these points that doesn't change depending on the angle you look at the paper, but that would change if you ...
0
votes
1answer
14 views

How could we define the existence of an object/element in the Euclidean space?

Let X be an object/element, What does it mean when I say "X is an object in the Euclidean space"? in other words, What differs an existed object from an unexisted one in the Euclidean space?
0
votes
1answer
41 views

Two equations have the same number of roots. [closed]

Find functions $f(x)$ such that $\forall\,(a;\,b)\ne (0;\,0)$ two equations $f(x)=ax+b$ and $x^2=ax+b$ have the same number of roots (real roots).
0
votes
0answers
14 views

Finding the dimensions of an open topped box

An open-topped box can be created by cutting congruent squares from each of the four corners of a piece of cardboard that has dimensions of 20 cm by 30 cm and folding up the sides. Determine the ...
1
vote
0answers
13 views

Topology of the intersection of toric arrangement

Hope someone will help me in the solution of the following question. I'm working on some topological problem involving the topology of the intersection of some characters of the torus. I want ot find ...
0
votes
0answers
15 views

Find number of triangle and quadrangles in $AG_2(3)$

$\textbf{Question-}$ Show that in $AG_2(3)$ there are - i) $72$ triangles ii) $54$ quadrangles iii) $4$ triangles in each quadrangle iv) $3$ quadrangles containing a given triangle My try- I know ...
0
votes
1answer
11 views

Length of Lace Algorithm

consider the following diagram depicting a shoe lace passing through holes. where starting width is 3, and ending width is 1 The width between nodes can either decrease or increase linearly or it ...
0
votes
2answers
31 views

Could the congruence of these two triangles be proven?

Using any of the known theorems(SSS, ASA, SAS, HL), Could it be proven that these two triangles(XBN, YWZ) are congruent? *Given: XB=YW,∠XBN=∠YWZ and XYZN is a rectangle.
0
votes
2answers
21 views

Find the area of the adjoining figure

In the adjoining figure, $ABCD$ is a trapezium in which $AB$$\parallel$$DC; AB=$7cm; AD=BC=5cm and distance between $AB$ and $DC$ is $4cm$. Find the length of $DC$ and hence, find the area of trap. ...
3
votes
3answers
324 views

Surface area of a sphere limits

If I am finding the surface area of a sphere in spherical coordinates my intergral would be like this: $$\int^{\pi}_0 \int^{2\pi}_0 R^2 \sin (\theta) d\phi d\theta =4\pi R^2$$ But if I do the ...
0
votes
1answer
36 views
+150

Defining ellipse using points and normal vectors from them

There is an article on how to detect circles in images using pairs of gradient vectors (assuming the circle is dark and background is bright). The thing is that gradient of image intensity at each ...
0
votes
0answers
24 views

Intersection of planes and lines [closed]

What is the intersection of two planes? What is the relation of the two lines that do not lie in the same plane and do not intersect?
0
votes
0answers
14 views

Find length of the midpoints of the diagonals in a given trapezoid [closed]

For any given trapezoid, where the bottom base, a, is larger than the top base b -- find the length of MN, the line connecting the midpoints of the diagonals, using only vectors.
0
votes
0answers
14 views

Permutation of conjoined faces in regular polygon with diagonals

I've been doing some study on relationships in polygons, right now, regular polygons. I've been trying to find relationships between the diagonals, angles, faces, vertices, and primarily conjoined ...
2
votes
1answer
25 views

Norm on $\mathbb R^n$ with given unit ball

Consider a finite subset $S$ of $\mathbb Z^n$ such that $-s\in S$ whenever $s\in S$ and $S$ generates $\mathbb Z^n$. What is a norm on $\mathbb R^n$ whose unit ball is precisely the convex hull of ...
0
votes
1answer
42 views

I need help finding the mean radius of a cylinder

The question is: What is the mean radius $\overline{r}$ from the midpoint of a cylinder of radius $a$ and height $h$ to its boundary surface? Evaluate $\overline{r}$ for $a = h/2 = 10~\mathrm{cm}$. ...
0
votes
0answers
14 views

A Geometry Terminology Question

Edges and diagonals are to polygons as faces and X are to polyhedrons? What is the answer to X? I've been touching up on geometry and I'm having trouble finding an answer to this, and inconsistency ...
0
votes
2answers
21 views

Configuration of five or more mutually equidistant points in space.

How is it proved that there is no configuration of five or more mutually equidistant points in $R^3$? Is it done by induction? I'm stuck. Help would be appreciated. Well, surely equilateral ...
1
vote
1answer
26 views

Probability of a random triangle containing the center of a polygon

Consider a regular polygon of $2n+1$ sides. Let three random vertices be chosen at random to get a triangle. The probability that the chosen triangle contains the center of the polygon is 5/14. What ...
3
votes
2answers
32 views

Triangle similarity question

I've been trying to solve this question for like 40 mins straight and can't seem to get anywhere. I tried drawing a parallel to |KM| from C to |AB| but that didn't seem to help. I just can't see a ...
-4
votes
1answer
55 views

University Question Regarding Circle Geometry [duplicate]

how would you recommend approaching this question: (http://i.stack.imgur.com/iM2Wk.png) I am fully aware of all the circle properties, but I am unsure how to get the angle DAC. Is this even needed ...
0
votes
0answers
24 views

How is the Uniqueness of Equilateral Tetrahedra Proved? [duplicate]

Equilateral tetrahedrons all have this property: For any two of its vertices exists a third vertex, which forms an equilateral triangle with these 2 vertices. (It doesn't necessarily have to be a ...
-2
votes
0answers
85 views

Circle geometry question. [duplicate]

I've been having trouble with this circle geometry question in my self-study beyond the course. I had stumbled across it an hour ago, but am not sure how to prove this. ...
0
votes
0answers
26 views

Find a point C on line segment AB such that line segment DC is perpendicular to AB. D is a point outside the line segent

Find a point C on line segment AB such that line segment DC is perpendicular to AB. D is a point outside the line segment. Note, Point A,B and C are in latitude,longitude format, i.e A = {lat,long} ...
2
votes
0answers
56 views

Beautiful problem about polyhedrons [duplicate]

A regular tetrahedron has this property: For any two of its vertices exists a third vertex, which forms a regular triangle with these 2 vertices. (But it doesn't mean any 3 vertices form a regular ...
0
votes
0answers
15 views

the Mahalanobis distance for 1D

I thought at the beginning that the Mahalanobis distance is only for more than or equal two variables until I found out a presentation for calculating the Mahalanobis distance for 1D. The formula is ...
0
votes
0answers
26 views

Produce one smooth curve on one triangle mesh

I hope to get one smooth curve on one triangle mesh. I get one path on the mesh at first. The path consists of vertices of the mesh. I can see the path from the image below. Each one green dot ...
0
votes
1answer
22 views

Given three concurrent lines $a,b$ and $c$, find the circunference tangent to $a$ and $b$ and with center at $c$

I have these three lines, and I need to construct a circumference tangente to two lines and that has center at the other line. I tried to construct the perpendicular lines that passes through the ...
1
vote
2answers
32 views

A new approach to the congruence of two triangles

I think that I've come to a new approach/theory to prove the congruence of two triangles: "Triangles are congruent if two pairs of corresponding sides and a non-included angle are equal in both ...
1
vote
3answers
63 views

Prove that if all triangles have the same angle sum then the sum of the angles in any triangle must be 180.

I don't know where to start. I know that the sum of the angles is less than or equal to 180. but how do i prove this.
0
votes
2answers
16 views

Given two points $A$ and $B$ and two distances $m$ and $n$, find a point that has distance $m$ fom $A$ and $n$ from $B$

I know that, as long as the distance from $|GI|<m+n$, as you can see in the figure $1$, I can constructo such point by the intersection of the circles with center at $G$ and radius $m$ and with ...
0
votes
0answers
8 views

The summit of a saccheri quadrilateral is greater than or equal to the base, and the midline is less than or equal to the legs.

Proof: Let ABCD be a saccheri quadrilateral with base AB. This means angle A= angle CAD (1) + DAB(2) =90. By Saccheri - Legendre the sum of the angles is less then or equal to 180. angle 1 + angle 2 + ...
-3
votes
1answer
57 views

What is the value of X in this? [closed]

How to find the angle $x$ in the following drawing? Does it help to note that : Sum of all angles of a triangle is $180^o$ The angle of a straight line is $180^o$
0
votes
1answer
46 views

The number Triangles in this picture [duplicate]

I want a method for find the number triangles in the under image.
-4
votes
3answers
45 views

Geometry: solving for $x$ given two angles in terms of $x$. [closed]

How would you find the value of x? What is the correct answer?
0
votes
0answers
21 views

Help required in kernel density estimation

In http://www.csc.kth.se/utbildning/kth/kurser/DD2427/bik08/LectureNotes/Lecture6.pdf Slide#3, the problem stated is that in $k$ nearest neighbor method assuming the d- dimensional data points are ...
0
votes
3answers
28 views

Perimeter & Area of a rectangle [closed]

The perimeter of a rectangle is 100ft. If its width is four times it length, what is the area?
1
vote
0answers
49 views

How to easily prove Euler's theorem, $OI^2=R(R-2r)$?

If $R$ is the circumradius and $r$ is the inradius of some triangle $ABC$, with its circumcenter being $O$ and incenter being $I$, then how to prove: $$OI^2=R(R-2r)$$ I have seen many mentions of ...