shape, congruence, similarity, transformations, properties of classes of figures, points, lines, angles
1
vote
0answers
9 views
Lamé parameters and distance on a curved surface
I was wondering if it is possible to compute the distance between two points which lay on a curved analytical surface. The surface is defined with differential geometry formulae (position vector of ...
1
vote
1answer
10 views
spherical coordinates of a unit vector around a normal N
So if I have a unit normal for a surface N(x,y,z) and an incident unit vector V(x,y,z) to that surface, how would I represent the vector V in spherical coordinates relative to the normal?
3
votes
0answers
25 views
Find the axis and angle of a sphere rotation.
A sphere is rotated a certain angle about some axis. Given two distinct points in a sphere, mark their original positions as $A$ and $B$, their positions after the rotation as $A'$ and $B'$. Using ...
2
votes
1answer
41 views
can I travel in the same direction along the surface of an ellipsoid without ever returning home?
Starting from an arbitrary point on an ellipsoid, moving straight at a random direction along the surface, are you always guaranteed to come back to the starting point eventually?
4
votes
2answers
40 views
Regular Pentagon is the Unique Largest Two-Distance Set in the Plane
A two-distance set is a collection of points for which only two distinct distances appear among pairs of points. (That is, the distance between any pair of points is either $x$ or $y$, and these ...
2
votes
2answers
26 views
Determinant in Line-Line Intersection
Assume we have two equations of a line,
$A_1 x + B_1y = C_1$ and
$A_2 x + B_2y = C_2$
Now we multiply the first equation by $B_2$ and the second by $B_1$ to obtain
(1) $A_1B_2x + B_1B_2y = C_1B_2$ ...
0
votes
1answer
25 views
Conceptually, how to deal with zero slope lines when using y=mx+b to drive other equations
I am (with wonderful help from this site) developing a number of VBA routines to drive some shape-related activity in Powerpoint. For example, I have a circle with a line segment that starts in the ...
0
votes
1answer
20 views
Finding the cross section of a couple of surfaces
$$x^{2}+y^{2}+z^{2}=4$$
$$x^{2}+y^{2}=1$$
$$x=0$$
$$y=0$$
$$y^{2}+z^{2}=4$$
How should I do this? I thought of, taking surfaces from the last one:
$y^{2}+z^{2}=4$ is a circle drew on the ZY plane, ...
1
vote
2answers
34 views
Perpendicular distance question?
I've been having trouble with the following question:
"The point $P(x,y)$ is equidistant from the lines $2x+y-3=0$ and $x-2y+1=0$, which intersect at $A$. Use the distance formula to show that ...
0
votes
2answers
24 views
Finding coordinates
The slope of the line passing through the point $(5,5)$ is $\dfrac 56$. All of the following points could be on the line except
A. $(2.5, 2) $
B. $(11, 10) $
C. $(8, 7.5) $
D. $(-1, 0) $
E. ...
0
votes
1answer
18 views
After subdividing a painted cube, how many smaller cubes have paint on exactly 2 sides?
A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2. How many of the smaller cubes have paint on exactly 2 sides?
Answer with illustrations will be helpful for ...
1
vote
2answers
26 views
Area of a parallelogram using Cross Product
How do you compute the area of the parallelogram with 4 arbitrary corners, say at (1,1,1), (2,3,4), (3,2,1), and (4,4,4) using a cross product? I understand with 3 corners but getting a little lost ...
1
vote
1answer
43 views
$360\times 60$ nautical mile is not equal with $6400$ km of earth radius
One degree on a great circle of earth equals to $60$ Nautical Miles. Hence:
$\ 360 \times 60 = 21,600$ M (Nautical Mile)
$\ 21,600M \times 1852$ Meters $= 40,003,200$ Meters $= 40,003.2$ Kilometers
...
1
vote
0answers
15 views
Mapping an object's projected 3D path to a pre-defined top-down 2D path.
The title of the question may be misleading and the context simpler. Please suggest more appropriate tags for this question.
Consider looking at a plane from two different perspectives.
Perspective ...
0
votes
0answers
19 views
Noncongruent arcs/angles and their degrees
I never learned Euclidean geometry, so I am working through Kiselev's books over the summer. I am curious about the following two questions:
Can two non-congruent angles contain 55 angular degrees ...
1
vote
1answer
17 views
Line segments- determine which 'side' each is on?
I have a master line segment, against which I am comparing 64 other child line segments. I have other criteria and have filtered out most of the child line segments (I have maybe 10 left).
I now need ...
0
votes
0answers
27 views
Affine transformation question
As a followup question to this question, I'm trying to figure out how to plug in my numbers to get my corrected value. So say I have a point on a line $A1=(10,12)$ which is my original point, and a ...
0
votes
0answers
22 views
Projecting a point onto ellipsoid
I have a best fit ellipsoid from a point cloud in the form of
$$Ax^2 + By^2 + Cz^2 +2Dxy + 2Exz + 2Fyz + 2Gx + 2Hy + 2Iz = 1$$
How can I project my points from my point cloud to my ellipsoid?
3
votes
2answers
46 views
Correction formula for two points
This is painfully simple- sorry for that- but I'm not a math guy and could use some help. Imagine I have a surface that goes from $(0,0)$ to $(100,100)$- a square. On it, I expect to find two points ...
0
votes
2answers
34 views
How do I show that an angle is a certain value in a triangle with two sides given?
In the following example I am told that angle x is 60° and that I have to prove it is (without a calculator). What is the simplest way of showing that it is true?
2
votes
1answer
37 views
Evaluating the value of CD
Any tips or solution will be welcomed. Do I need to find sector area to evaluate the length of CD?
3
votes
0answers
51 views
A problem on probability theory and geometry
I am stuck on the following problem: given a circle of radius $R$ I put randomly $N$ points inside the circle. What is the probability to have the distances of every point from the other greather than ...
5
votes
4answers
449 views
What could be a homeomorphism from the circle to a triangle?
I'm looking for a bijection from a circle to a triangle that is continuous with a continuous inverse. What could be one?
1
vote
1answer
53 views
Lines and Planes
can someone please help me? How can I find the equation of the plane which contains the line
$r:$ $ x= 2 + 2\lambda$
$ y= 3 - \lambda$
$ z= -3\lambda$
($\lambda$ is a Real number)
and ...
6
votes
0answers
95 views
What’s the best way to cut an apple?
Take the apple in one hand, and the knife in the other. In the first cut, the apple is divided in two pieces: a small one that drops into the plate and a big one that is still hold with the hand. This ...
1
vote
1answer
47 views
Lines and planes at space
First of all, sorry for my poor English.
Can someone please help me?
How can I find the parametric equation of the line that have $ A=(1, -2, -1) $ and passes through the skew lines
$r:$ ...
2
votes
2answers
66 views
How to find the centre of mass of an equilateral triangle?
I have a pentagon lamina with all the sides length 8cm to find the centre of mass of the pentagon do you do:
$$\frac{4+8+ \frac{1}{3}*something?}{8^2+16\sqrt3}$$
A uniform lamina ABCDE consists of a ...
2
votes
2answers
48 views
Area puzzle in colored triangle [duplicate]
I have tried to figure out by calculating the area but I got same results for these, so where is gone the hole?
0
votes
0answers
6 views
questions about parametric equation for an affine space $\mathcal{A}$ and $\mathcal{F}=(O;e_{1},e_{2},e_{3})$ a cartesian frame in $\mathcal{A}$
Let $\mathcal{A}$ be a $3$-dimensional affine space and $\mathcal{F}=(O;e_{1},e_{2},e_{3})$ a cartesian frame in $\mathcal{A}$.
1.) Determine the parametric equation
2.) The determinant form ...
0
votes
2answers
29 views
Calculating interior angles of quadrilateral
stupid question... but:
I've a polygon which has the points $(a_x,a_y),(b_x,b_y),(c_x,c_y), (d_x,d_y)$
How can I calculate each interior angle of this quadrilateral? I know that in sum, it has to be ...
0
votes
0answers
16 views
Calculating inner angles, length, area of polygon from gps coordinates
I've a set of polygons. Each polygon is described by 4 Points (Longitude,Latitude).
How can I calculate the area of the polygon, the inner angles of each angle and the length of all sides and finally, ...
1
vote
1answer
44 views
Texture mapping and conformal transformation
I'm a 3D programmer with background in physics, interested to better know how texture mapping can be made using conformal maps for simple surfaces.
I want to texture map a paraboloid:
...
2
votes
1answer
57 views
Draw a regular hexagon in simcity
I know how to make a pentagon (there are youtube videos), and I kinda thought I knew how to do a hexagon using 5 circles:
one in the center, shift-drag 2 guide blocks.
2 below it, each shift-drag 2 ...
0
votes
1answer
26 views
Coordinate Geometry Problem
I have a question that I've started at school but had couldn't figure out what to do or where to start.
Sorry, I don't have the question written down, just the image.
...
0
votes
1answer
30 views
Why is the length R cosine theta?
Why is the length described as R cosine theta (the top where the Sphere is sliced off)? I've been staring at the geometry for quite a bit & can't figure.
Thanks
2
votes
0answers
44 views
$\operatorname{Hom}_{\mathbb{Z}_2}(S^n,\mathbb{R}) \simeq S^n \times_{\mathbb{Z}_2} \mathbb{R}$
Let $\operatorname{Hom}_{\mathbb{Z}_2}(S^n,\mathbb{R})$ the set of $\mathbb{Z}_2$-maps from $S^n$ to $\mathbb{R}$ and $S^n \times_{\mathbb{Z}_2} \mathbb{R}$ the fiber product of $S^n$ and ...
0
votes
0answers
47 views
A line through the centroid G of $\triangle ABC$ intersects the sides at points X, Y, Z.
I am looking at the following problem from the book Geometry Revisited, by Coxeter and Greitzer. Chapter 2, Section 1, problem 8: A line through the centroid G of $\triangle ABC$ intersects the sides ...
2
votes
0answers
51 views
Which algorithm partitions the surface of a sphere in a meaningful way?
Edit: As suggested I have tried to describe my problem in a more formalistic way. Please bear with me, since neither english nor math are my native languages ;-) For the applied problem please see ...
3
votes
1answer
51 views
Proof of “triangles are similar iff corresponding angles are equal”
I'm looking for a basic proof of the basic plane Euclidean geometry theorem: Two triangles are similar if and only if their corresponding (interior) angles are equal.
(The theorem can be also worded ...
-3
votes
1answer
40 views
Area between concentric circles [closed]
We are given two concentric circles k1 and k2. Chord t=10cm of the bigger circle is tangent of the smaller circle. Find the area of ring between two circles.
0
votes
0answers
46 views
Finding if the Point is in the triangle
Can You Please tell me if this is right
Point(x,y,z) triangle points ABC
using co-planer
determinant
|x-Ax y-Ay z-Az|
|x-Bx y-By z-Bz| = 0
|x-Cx y-Cy z-Cz|
then the point is in the tringle
2
votes
3answers
50 views
A question on geometry?
I wanted to know, given quadrilateral ABCD such that $AB^2+CD^2=BC^2+AD^2$ , prove that $AC⊥BD$ .
Help.
Thanks.
0
votes
1answer
43 views
3D Cartesian Transformation
I have a tetrahedron in a 3D Cartesian space.
It has two orientations.
I know the same three vertices positions (xyz) in the first orientation and the second orientation.
I know the position of the ...
1
vote
1answer
27 views
Proof convex polyhedron with line does not contain a corner if closed
The excercise I am struggling with is the following: Given a convex closed polyhedron that contains a line, the question is, whether this polyhedron can also contain a corner.
My idea was to make a ...
1
vote
1answer
30 views
How to position rectangles such that they are as close as possible to a reference point but do not overlap?
Given a set of rectangles contained within a larger rectangle such that none overlap, what is the most efficient way to determine the position of a new rectangle such that it is as close as possible ...
2
votes
1answer
47 views
Coincidence of triangle centres
There are a number of results in triangle geometry of the type: if two specific centres (as a concrete example, the incentre and the circumcentre) coincide, then the triangle is equilateral. Does ...
17
votes
5answers
476 views
Is there a deep reason why $(3, 4, 5)$ is pythagorean?
The triple $(3, 4, 5)$ is a pythagorean triple - it satisfies $a^2 + b^2 = c^2$ and, equivalently, its components are the lengths of the sides of a right triangle in the Euclidean plane.
But of ...
0
votes
0answers
34 views
Is the total solid angle of a point always $4\pi$?
If I have a point at the center of a sphere, then the total solid angle of this point is $4\pi$. If I now put, instead of a sphere, a cube around the point, the total solid angle in ragard to the $6$ ...
1
vote
1answer
26 views
Geometry: Measurements of right triangle inscribed in a circle
So, I've got a triangle, ABC, inscribed in a circle--Thale's theorem states that it is therefore a right triangle. It is also given that $\overline{BA}$ is the diameter of the circle, and hence angle ...
0
votes
1answer
22 views
How to find the area of a shape whose sides are made up of line or arc of circle? [closed]
The arc and lines form the sides of the shape.
The sides touch each other at end point in such a way that each end point can touch only one shape
and the shape is closed
eg:- ...
