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
0answers
15 views

A question about plane curve

This is an exercise in do Carmo's differential geometry of curves and surfaces (exercise 1.7.7). Let $\alpha:\mathbb{R}\to\mathbb{R}^2$ be a plane curve defined in the entire real line $\mathbb{R}$. ...
0
votes
2answers
14 views

line segment intersection

Do these two line segments intersect ? I'm confused because if you extend the below line then they will intersect otherwise not but we can't extend them as they are line segments. Is line segment ...
1
vote
1answer
17 views

Prove uniqueness of polar-coordinates $(R>0, \theta)$ up to angle $\theta+ 2 \pi$.

Prove uniqueness of polar-coordinates $(R>0, \theta)$ up to angle $\theta+ 2 \pi$. Suppose we have $(x,y) \in \mathbb R^2$. Then we can transform this point to polar-cordinates $(R>0, ...
1
vote
1answer
22 views

Mapping a distorted ellipse onto a circle

I have a circular label pasted on a cylindrical object. In the image, this circle looks like a asymmetrical ellipse. I know the radius of the cylinder and that of the label. What mapping do I need to ...
1
vote
1answer
32 views

Euclidean Geometry problem: prove that $C'$ is the midpoint of $A'B'$.

The tangents to a circumference centered at $O$, passing through an exterior point $C$, meet the circumference at the points $A$ and $B$. Let $S$ be an arbitrary point on the circumference. The ...
3
votes
0answers
47 views

History of math geometry problem

Here is a problem I am working on from a history of math course: And here is some of my work at least the setting up to try to work with angles to work through parts (b) (c) and (d): I see how ...
1
vote
1answer
17 views

expected size of a special set of random points in the unit square

Today I came up with this fun problem, but I'm having a hard time to solve it completely myself. The question is the following: Let's generate n random points ...
2
votes
1answer
25 views

Validity of proof for surface area of a sphere [duplicate]

On a geometry test I forgot the formula for the surface area of a sphere so I derived it and ended up being right. But it seems like my derivation is wrong. I got the surface area formula by taking ...
0
votes
0answers
14 views

Calculating longitudinal and latitudinal coordinates on a plane

I have a latitude and longitude coordinate. What I'd like to accomplish is extend on a straight line in any direction 75 Miles, so for instance 75 Miles East or ...
0
votes
0answers
13 views

Geometrical place involving circles. [duplicate]

How to find the equation of the geometrical place of all centers of a circles that tangent from inside to the circle $x^2+y^2=R^2$ and the $y$-axis? (Suppose that $x,y\geq 0$)
0
votes
0answers
43 views

Find the area and the measure of interior angles of the rhombus $ABCD$

I have such a problem which I am really earnest to solve, but I got stuck and hope you'll help me to find a solution: So we have a rhombus $ABCD$(in it a circle is inscribed) in which ,we see from ...
0
votes
1answer
8 views

Non constant function of two points invariant under Affine transformation proof

Here is the question; Prove that there does not exist any nonconstant function of pairs of distinct points $P,Q\in\mathbb{R}^2$ or of triples of distinct non collinear points $P,Q,R\in\mathbb{R}^2$ ...
3
votes
3answers
57 views

Nice parameterization of $x^2 + y^2 - kx^2y^2 =1$

Can anyone find a nice simple parameterization of this curve. Just the quarter where $x \ge0$ and $y \ge0$ would be fine. The parameterization should be "nice" in the sense that the first derivative ...
0
votes
1answer
12 views

Radius of a circle (partially) inscribed off-centre in a square

Suppose we have a square diamond. There is a circle, where the top point of the circle is at the top corner of the diamond, and it touches the bottom two sides of the diamond. What is the radius of ...
5
votes
2answers
48 views

Geometry after Khan academy's tutorials

I always liked geometry at school, so by the side of my normal studies I've been going through the Khan academy videos. Could anyone suggest some good books that takes these geometry topics further? ...
1
vote
0answers
37 views

The Least Area For a Needle to Pass Through a Curve?

I don't know if this question is a famous one. One of my fellows asked me these questions to tease me, but I was able to find a solution for only one of these: There is one needle of length $2$ ...
1
vote
2answers
45 views

Finding a normal to an ellipsoid

Let $E$ be an ellipsoid centered at $v = (x,y,z) \in \mathbb{R}^3$ and let $T:\mathbb{R}^3 \to \mathbb{R}^3 $ be a linear transformation which transforms $E$ to a sphere $S$ with a radius of length ...
0
votes
1answer
28 views

Trying to revise a formula I was once given. How many rectangular prisms are in a $n \times n \times n$ cube?

I post it the other day. The only answer I got is that the total number of rectangular prisms in a cube is equal to ${n+1 \choose 2}^3$. But using $n=2$, I found the formula to be wrong. When counting ...
1
vote
0answers
13 views

Lateral area of a cone with oblique base (elliptical base)

Can someone help me find the lateral area of a straight circular cone with oblique base ( inclined elliptical base) as seen at the following link. ...
0
votes
1answer
49 views

Generalised Pythagorean Theorem?

$|a+b|^2=|a|^2+|b|^2+2 Re(\overline ab)$ Can anyone explain this equality to me? How it is derived?
0
votes
1answer
29 views

Converting 3D into 2D

I have a quad and I'm trying to convert its vertices so that they're facing the camera which is lying at 0,0,1 looking down the Z, or not even specifically facing the camera, just so they're facing up ...
4
votes
2answers
32 views

Why do folded concentric circles and rectangles form a hyperbolic paraboloid?

Here is a "self-forming" origami that I made from folding concentric circles - it would also happen if I folded concentric rectangles. How can the fold shapes such a saddle-like geometry?
0
votes
0answers
31 views

Prove equality of angles in parallelogram

In a parallelogram $ABCD$, $P$ is a point inside the parallelogram such that $\angle APB + \angle CPD=180$. Prove that $\angle PDC=\angle PBC$.
5
votes
2answers
49 views

How to characterize rotations in $\mathbb{R}^n$?

I am studying the performance of an optimizer algorithm to find the $$ \textrm{argmin}_{x\in \mathbb{R}^n} f(x) \text{ where } f : \mathbb{R}^n \rightarrow \mathbb{R} $$ I would like to test how the ...
2
votes
3answers
34 views

Complex Numbers of Unit Modulus

if $z_1$, $z_2$ and $z_3$ are Complex Numbers of Unit Modulus Such That: \begin{equation} |z_1-z_2|^2+|z_1-z_3|^2=4 \tag{1} \end{equation} Find the value of $$|z_2+z_3|$$
1
vote
0answers
30 views

Proof: Convex set of a quadrilateral is a convex quadrilateral

Prove that $\Box ABCD$ is a convex set whenever $\Box ABCD$ is a convex quadrilateral. Things I know: A set of points $S$ is said to be a convex set if for every pair of points $A$ and $B$ in $S$, ...
0
votes
0answers
23 views

Question on geometry based on Ceva's theorem

Prove that cevians perpendicular to the opposite sides are concurrent. Note:I know that they are perpenducular because they pass through the orthocenter. But I actually want to know how to write ...
1
vote
4answers
33 views

prependicular Vs prependicular bisector

We have $AH=HB$ and $BG=GC$ in the image below. Why is $AD=2\times FG$?
0
votes
1answer
20 views

3d analogue of an ellipse

An ellipse is the set of all points X in 2d space such that the the sum of the distances AX and BX is a given constant constant, where A and B are given points. What is the name for the set of all ...
4
votes
2answers
93 views

Relationship between circles touching incircle

I am trying to derive a relation between radius of those outer circles and radius of the incircle. Those outer circles are tangent to the incircle and respective sides. I have tried and failed ...
1
vote
0answers
37 views

Staircase Lemma

Let $S$ be a staircase-shape contained in the north-eastern quarter-plane. Let $k$ be the number of its south-western corners. In the staircase shown below, there are $k=4$ corners: In each corner ...
0
votes
1answer
35 views

Transformation of 2D profile to 3D coordinates

I am sure that answer for similar questions have being given more than one thousandth times, but correct answer that suits my needs I still haven't found. Currently I am developing simple 3D app. My ...
0
votes
0answers
25 views

Help solve a geometry question involving circles and triangles [on hold]

To clarify, AB = 9, BP = 13 and PQ is tangent to circle. Find the length of PQ
0
votes
0answers
44 views

I need a thorough explanation for a answer I was given not long ago.

The other day I have gotten an answer from one of my answerers regarding the question how many pyramids in a square based pyramids. He explained in the following words… basically imagine a pyramids ...
1
vote
2answers
27 views

Looking at an angle rotated

Suppose you have an angle of degree theta painted on the ground at a spot. You are standing d distance away and looking at it from a height of h and from your perspective the angle appears to be of ...
0
votes
1answer
37 views

convex hull function in matlab

Is there anyway to compute the convex hull of a finite set of points in Matlab and gives the half-space representation as its result? I usually use a toolbox called MPT developed at ETHZ Zurich, but ...
0
votes
1answer
26 views

Altitudes of Triangle

I have a triangle defined as 3 lines, each defined by two coordinate points A and B. I have the area of the triangle but need to calculate the 3 altitudes and their respective sides A and B points. ...
0
votes
2answers
67 views

Sketching phase portraits [on hold]

I am trying to answer this question: I would like to know how I go about drawing a phase portrait. All of the examples in my notes are simply the solution with no explanation, and this method of ...
5
votes
1answer
96 views

How can a simple closed curve not look locally like the rotated graph of a continuous function?

A simple closed curve is a continuous closed curve without self-intersections. The question of whether you can inscribe a square in every simple closed curve is currently an open problem, but this ...
0
votes
2answers
24 views

Optimization of the surface area of a open rectangular box to find the cost of materials

A rectangular storage container with an open top is to have a volume of 10 cubic meters. The length of the box is twice its width. Material for the base costs ten dollars per square meter and for the ...
-2
votes
0answers
31 views

Can someone solve this geometry question (Grade 9) [on hold]

Geometry A field is in the form of an isoceles trapezium ABCD Given: AB = 15m The perimetre of the field is 35 m. Calculate AD, DC, CB. Thank you very much
0
votes
0answers
42 views

compact surface of revolution

I have to prove that a compact surface of revolution is diffeomorphic to a sphere or to a torus. And show that $\int_{S} K dA= $ =$\{4\pi,$ if S is spherical type 0, if S is toric type $\}$, ...
0
votes
0answers
29 views

Decide coordinates for a vector in a triangle (Image attached)

I have the following triangle. I have to express the line $\overline{AT}$ as a linear combination of $\overline{AC}$ & $\overline{AB}$. A hint was to use the knowledge of $\overline{AT} = ...
4
votes
2answers
106 views

How find the $AP+\frac{1}{2}BP$ minmum value

An equilateral triangle $ABC$ such $$AB=BC=AC=2a>0$$ A circle $O$ is inscribed in triangle $ABC$,and the point $P$ on the circle $O$. Find the minimum $$AP+\dfrac{1}{2}BP$$ My idea: let ...
0
votes
1answer
14 views

How many tetrahedrons an edge belongs to in a Body-Centered Cube Lattice?

Body-Centered Cube Lattice, also known as BCC Lattice (shown in the Figure) is a kind of lattice where the body of a cube also contains a vertex. 4 vertices as the figure shows constitute a ...
2
votes
0answers
63 views

Proving there is no set of five distinct points s.t. every three points are the vertices of a right triangle.

We can see that the following proposition is true. Proposition : Each triangle $ABD, ACD, BCD$ is a right triangle for $$A(0,b,0), B(a,0,0), C(0,0,0)\ \ \ (a\gt 0, b\gt 0)$$ $\iff D$ is either ...
1
vote
2answers
28 views

Find perimeter of traiangle when you know two sides

Here's the GRE problem: The length of one side of a triangle is 12. The length of another side is 18. Which of the following could be the perimeter of the triangle? ...
1
vote
1answer
39 views

Flat Surfaces in $\mathbb{R}^3$ Can Be Bent Only Along Straight Lines

This is a problem out of Elementary Differential Geometry by Barrett O'Neill (Chapter 6 Section 3 Number 2). Let $M$ be a flat surface in $\mathbb{R}^3$ with principal curvatures $k_1$ and $k_2$, ...
0
votes
3answers
54 views

Show that there are exactly two lines through a point p outside the circle that are tangent to the circle C

Let $C$ be a circle of radius $r$ in the plane. Let $p$ be a point in the plane that lies outside of $C$. Show that there are exactly two lines through $p$ that are tangent to $C$. It is one of ...
0
votes
3answers
81 views

Is there any geometry where ratio of circle's circumference to its diameter is rational?

In Euclidean geometry, the ratio of the circumference of a circle to its diameter is an irrational number, 3.14159 and so on. But if you change to non-Euclidean geometries, you get other values for ...