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
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
30 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
51 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 ...
-2
votes
4answers
32 views

Perimeter of a rectangle from Area [closed]

How do you find the Length and width of a rectangle when given the area?
0
votes
2answers
13 views

In Fig.9.17. PQRS and ABRS are Parallelograms and X is any point on side BR.

In Fig.9.17. PQRS and ABRS are Parallelograms and X is any point on side BR. Show that i)ar(PQRS)=ar(ABRS) ii)(AXS)=$1/2$ar(PQRS) I have no clue.
1
vote
1answer
14 views

Determine the isometric group $G$ which transfers a square into it self

I am solving the following exercise: Determine the isometric group $G$ of the euclidean plane which transfers a square into it self. The restriction of an element $g \in G$ on the vertices of ...
-5
votes
1answer
64 views

Geometry problem.

I have to find what is theta($\angle$GOE = $\angle$CDE). Here is a condition for above shape: The shape OCG is a quarter of unit circle(center is O). The line DF is a tangent line of curve CG ...
0
votes
0answers
5 views

Are fiber products in the category of locally ringed spaces always fiber products in the category of schemes?

Such a conclusion is made in the proof of proposition 4.20 in the book "Algebraic Geometry I " by Goertz - Wedhorn without proving that the fiber producct in question is a scheme. Is such an argument ...
0
votes
2answers
70 views

Prove that circumference of circle with radius $r$ is $2r\pi$

Prove that circumference of circle with radius $r$ is $2r\pi$. I tried this way: let $a$ be the edge of right $n$-th sided polygon inscribed in circle with radius $r$. Let $O$ be the center of this ...
0
votes
0answers
29 views

Area of a circle of Radius “r” in a rectangle

This is a very basic problem but i would like to ask as i am unable to resolve it. I have a rectangle of the following dimensions. $Length = L$ $Width = W$ I picked a point ($x,y$) in this ...
2
votes
1answer
31 views

Does a unipotent transformation preserve covolume?

Let $S\subset \mathbb{R}^d$ and define $v(S)$ to be the volume of the set $(S+\mathbb{Z}^d)\cap [0,1]^d$ (where $[0,1]^d$ is the unit cube $[0,1]\times [0,1] \times...\times [0,1]$). Let $T: ...
0
votes
2answers
18 views

Speed and length of the shadow relationship proble

A girl of height $0.9 m$ is walking away from the base of a lamp-post at a speed of $1.2 m/s$. If the lamp is $3.6 m$ above the ground, find the length of her shadow after $4$ seconds. I calculated ...
1
vote
1answer
45 views

Comparing fractals

Is there a way to compare if two fractals are "isomorphic"? I'll give an example of what I mean. Consider the following two fractals. First we have the Sierpinski triangle, and next we have the ...
3
votes
2answers
34 views

Number of Curvature Maxima of a 2D Cubic Bezier curve

I am trying to prove that a standard cubic Bezier curve can only have at most 2 curvature maxima over $t \in [0,1]$. Assuming that no 3 adjacent control points are colinear, the curvature will either ...
0
votes
1answer
26 views

Discuss the following graphs(Differential Equations)

So I have a differential equations midterm coming up soon, and in my last exam I messed the graphing question up. It was very similar to the one I am posting. All the questions said was "Discuss the ...
0
votes
0answers
20 views

Coordinate function in Synthetic Geometry?

Let A and B be distinct points in the plane P, let l = line AB, and assume that distance AB = 1. Prove that there exists a coordinate function f: l-->R such that segment AB = {P E l: f(P) E [0,1]} ...
0
votes
0answers
21 views

Using trilateration with unknown points to determine change in position

I have multiple fixed points to which I know the distance. I do not know the position of these points before hand. I will know my absolution position (using other means) at the start, but afterwords I ...
2
votes
0answers
26 views

Launch angle required to hit coordinate (x,y) with air resistance

Finding Angle of Elevation to hit X, Y and Wikipedia Angle required to hit coordinate work, but don't calculate air resistance. Is there a way to find the launch angle of a projectile required to hit ...
2
votes
1answer
32 views

Riemann manifolds exercise

I struggle with this exercise from Riemann Manifolds: Introduction to Curvature by Lee: A curve $\gamma: [0, b) \to M (0 < b \leq \infty)$ is said to converge to infinity if for every compact ...
0
votes
2answers
29 views

In Fig. 9.16, P is a point in the interior of a parallelogram ABCD.

In Fig. 9.16, P is a point in the interior of a parallelogram ABCD. Show that i)ar(APB)+ar(PCD)=$1/2$ar(ABCD) I have no idea how to solve this. A little help would be appreciated. Thank you!
1
vote
1answer
43 views

Euclidean geometry question

Let $(P,L,\varepsilon)$ be a plane with finitely many points (i.e $P$ is finite) Assume in addition to the axioms of incidence that for each $Q \in P$ and $l \in L$ with $Q \not\varepsilon l$ there ...
0
votes
1answer
23 views

Find the given side of the following diagram

In Fig. 9.15, ABCD is a parallelogram, AE $\perp$ DC and CF $\perp$ AD. If AB$=16$ cm, AE$=8$ cm and CF$=10$ cm, find AD.
0
votes
0answers
16 views

Quartic curves with four connected components

A quartic plane curve in $\mathbb{RP}^2$ can be defined by a quartic equation $F(x,y,z)=\sum a_{ijk}x^iy^jz^k$ with 15 coefficients. Now let's focus on smooth quartics that have a maximal number of ...
0
votes
0answers
20 views

Intersection point of two right cones and plane orthogonal to cone base

How to find an intersection point $X$ of two right cones intersection (brown dashed line) and a plane orthogonal to cone base plane? Lets say $A = (a_1, a_2, a_3)$, $B = (b_1, b_2, b_3)$ and $L^a, ...
2
votes
0answers
30 views

Show the Hausdorff dimension of a set of numbers with digit 5

I can show heuristically that the answer is $log(9)/log(10)$ but I am struggling to prove this rigorously. This is using the construction that after the first iteration we have $9$ intervals, length ...
0
votes
0answers
21 views

About Geodesic polar coordinate

What is different from geodesic polar coordinates and other polar coordinates? Geodesic polar coordinates has a form of $$ds^2=dr^2+f(r,\theta)^2\,\,d\theta^2$$ In $S^2$, $f(r,\theta)=\sin(r)$ which ...
1
vote
1answer
26 views

Geometry circumsribeable polygons and angle measures

$ABCDEF$ is a circumscribed hexagon. It is known that $AB=2 BC=3 CD=2 DE=5 EF=7.$ Find $FA$. I can't find any theorem relating to polygons only for quadrilaterals that is the sum of opposite sides ...
0
votes
0answers
15 views

Direct computation of hyperboloid-line intersection in 3d

I was wondering if a solution to this problem that doesn't involve coordinate space transformations. I have two points in 3d space, and am interested in locations where the difference of the ...
1
vote
1answer
10 views

Relation between midsegment of a trapezoid and midsegment of the diagonals

In any given trapezoid, is the midsegment of the entire trapezoid collinear with the midsegment of the diagonals?
0
votes
0answers
15 views

How do I define a three space?

I'd like to take a hierarchically-modeled (vertices, lines, faces, etc) 4D object and find its intersection with three-space. In Paul Isaacson's thesis, Computer Graphic Presentation of Hypothesized ...
2
votes
1answer
99 views

Number of Distinct Regular n-gons, given n

Is there a formula to find the number of distinct regular n-gons possible, given n? And by distinct, I mean disregarding anything like reflections or rotations. Working it out, I find the following ...
4
votes
4answers
84 views

Equation of a line tangent to circumference

Discover the general equation of the tangent line to the circumference $x^2 + y^2 - 2x + 4y + 1 = 0$ by the point $(3,4)$. NO CALCULUS. by the circumference equation i discovered that $C(1, ...
0
votes
3answers
41 views

Prove that for positive $a,b,c : a^2+b^2=c^2\Rightarrow a+b < c \sqrt 2.$

Prove that for positive $a,b,c : a^2+b^2=c^2\Rightarrow a+b < c \sqrt 2.$ Is it solved considering a right isosceles triangle? I'm stuck on it
2
votes
3answers
251 views

What is the geometric interpretation of the following equation?

What is the geometric interpretation of the following equation? $\displaystyle\left|\frac{1+z}{1-i\bar{z}}\right|=1$
0
votes
1answer
49 views

How can I compute angles & lengths of the following tiling shape

a while back I created a tile made of arrows: I did it using a vector graphics software, without really understanding the properties of this shape. Now, let's say I want to write a program to ...
2
votes
3answers
81 views

Problem about right triangles.

Given N>1 right triangles. Sum one legs of each of them, then sum all the left legs, then sum all hypotenuses. These 3 sums form the sides of a right triangle. Prove all given N triangles are similar ...
0
votes
1answer
26 views

I am making a study about connecting the unfolded square pyramids, can you help or suggest something?

I am making a study about connecting the unfolded square pyramids, or simply connecting the vertices of the nets of the square pyramid, and my goal now is to find the area of the unoccupied space when ...
0
votes
0answers
35 views

Verify f is a coordinate function

If $l$ is a nonvertical line in the Cartesian Plane then $l$ has an equation of the form $y=mx+b$. Define $f:l \rightarrow \mathbb{R}$ by $f(x,y)=2x \sqrt{1+m^3}.$ Verify that $f$ is a coordinate ...
0
votes
0answers
52 views

Klein bottle visualization, parameterization, and isotropic version

Suppose a bright glowing orange mobius strip appeared in space for just an instant and then disappeared, except for its glowing orange edge, which remains suspended motionless in space for a moment, ...
0
votes
1answer
38 views

When are two submanifolds “the same”?

Consider two smooth submanifolds $N\subseteq\mathbb R^n$ and $M\subseteq\mathbb R^m$. Let there be a function $\varphi\colon N \to M$ that is bijective. Which properties does the function $\varphi$ ...
4
votes
4answers
801 views

Can the distance between two points equals zero

Can the distance between two point on a plane be zero? I just assumed yes but I have heard the argument no because if the points are in the same location then they are the same point and thus you are ...
2
votes
0answers
51 views

Zeros of a holomorphic function.

Let $X$ be a connected complex manifold with dimension $n \geq 1$ and $f:X \rightarrow \mathbb{C}$ be a holomorphic function. Suppose that on a coordinate open set $U$, the function takes infinitely ...
0
votes
0answers
31 views

Roulette of a parabola - Delaunay-Surface

I've problems to understand an equation I've found in various books and papers. Maybe someone could help me and explain it a little bit more precisely. I colored the equation in yellow (the picture ...
2
votes
1answer
48 views

Proving $R +r\le h_{max} $

If $R$ is the circumradius , $r$ the inradius and $ h_{max}$ is the largest altitude of acute angled triangle $ABC$, then prove that $$R +r\le h_{max}. $$ I tried this using Euler's inequality but I ...
0
votes
2answers
29 views

Calculate an edge of a cube

The question is: How far the edge of the cube is increased knowing that if the $2\text{ cm}$ edge of the volume is $2402 \text{ cm}$ ? I already found that an edge is $(x+2)^3$ but I can't find the ...
0
votes
0answers
46 views

What makes a line “straight”?

In Euclidean space, there can be several definitions that makes a straght line: Line of shortest distance between two points Line that is linear, i.e with the points satisfying a linear equation ...
1
vote
0answers
14 views

Huygens formula

Let AB - arc of the circle , and the scale degree of the arc, and as the radius of the circle are unknown . For approximate calculation of the length of the arc used as follows. Notes on the arc of ...
1
vote
1answer
15 views

proving an vector indentity in triangle [closed]

P is a point in triangle ABC,to prove that $$S_{\triangle PBC}\cdot \overrightarrow{PA}+S_{\triangle PAC}\cdot \overrightarrow{PB}+S_{\triangle PAB}\cdot \overrightarrow{PC}=\overrightarrow{0}$$ ...