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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1answer
43 views

Is there an equation to find the angle of the diagonal in a rectangle?

If we have a rectangle of length 5 and height 5 the angle of the diagonal would be 45°. We know this is true but how can we arrive at this conclusion mathematically?
0
votes
1answer
22 views

Rotating a plane defined by a normal and a distance from the origin around an arbitrary point in 3D space

I have a plane defined by its normal and its distance from the origin. I have a rotation matrix and a point in 3D space around which to do the rotation. What formula will allow me to do the rotation? ...
1
vote
2answers
50 views

A simple geometry question

Suppose $ABC$ is any triangle and $BE$ is any line from the vertex $B$ to a point $E$ lying inside the segment $AC$. Let $D$ be any point on $BE$. I would like to verify the following: regardless of ...
3
votes
3answers
62 views

Geometry - Proof involving a triangle inside another triangle.

https://imageshack.com/i/p5KYsbcIj Here is an image of my picture. If its given that $AE = DC$, prove that $AB + BC > EB + BD$. My idea was to construct a parallelogram out of each triangle so ...
1
vote
1answer
20 views

How would I normalize the slope of a line?

Assuming I have different lines with different slopes, I would like to compare the slope of each line as relative to one another. The program I am currently writing needs to compare the slopes of the ...
0
votes
1answer
34 views

Projecting line onto edge of ellipse?

I feel like the answer to this should be fairly simple, but I am absolutely hitting a brick wall here. I have a line, with angle $\beta$ and origin $(x_l, y_l)$. I have a rotated ellipse, with major ...
1
vote
1answer
45 views

What is the difference between Congruent and equal?

What is the difference between equal and congruent? When I should say that the two figures are congruent or equal ( identical)? What is the difference between them. Can somebody please explain me with ...
0
votes
1answer
17 views

Find the locus of the the vertex A.

Consider $\triangle ABC$. BC lies on a line passing through $(g,f)$. The pair of straightlines $(x+y)(x-9y)=0$ are the perpendicular bisector of sides AB and AC of $\triangle ABC$. Find the locus ...
2
votes
1answer
58 views

In terms of Plane Geometry - why the area of any known figures are in the square units ( why do we multiply)?

By area, I mean that the space occupied by any shape. For example, the space occupied by the rectangle - is length multiplied by breadth. If I don't consider volume - or I consider the thickness has ...
0
votes
3answers
34 views

how to find the angle between line and x-axies

I have an 2 GPS coordinate which represent an start and end point of line so how to find the angle in image ??
0
votes
0answers
20 views

Create dynamic cities of perspective angle x

I'm creating a tilemap... I found you can create unique building sizes with perspective with six tiles using parallel projection, whose angles are always 45 degrees... this allows you to connect to ...
3
votes
1answer
51 views

How can I prove this proposition that seems obvious?

The following problem seems obvious: If $\triangle ABC$ and $\triangle DEF$ are such that $|AB|=|DE|$ and $|BC|=|EF|$ but $\angle ABC > \angle DEF$ then $|AC|>|DF|$. But I can't to write ...
1
vote
1answer
31 views

Bounding volume of catmull-rom splines

I need to compute a 2D "spherical" bounding volume for the part of a catmull-rom spline $S(t)$ with four control points $P1$, $P2$, $P3$ and $P4$ in the domain $0 \le t \le1$. The purpose is to reduce ...
0
votes
0answers
28 views

3D Vector projection on a Plane

I want to Project a Vector on to a Plane. Assume, you have a Central Point (1,1,1) and you want to move (0,0,3) in z-direction. How can I project the end of this movement (point) on a plane with ...
0
votes
0answers
24 views

What is the surface area for a hypercube? [duplicate]

I am doing a project on the fourth dimension and I need to find the surface area of a hypercube. How do you do it? Can anyone explain where the expression $(x+2)^n$ comes from and how can it help ...
-2
votes
1answer
34 views

The locus of points with given sum of squares of distances to two fixed points

$A(a,b)$ and $B(b,-a)$ are two fixed points. If $P(x,y)$ is a moving point such that $$|AP|^2 + |PB|^2 = |AB|^2 \tag1$$ prove that $x^2 + y^2 =(b-a)(x+y)$. So far I tried to use distance formula ...
0
votes
1answer
30 views

how to find triangular point from a side

i have two triangles. Say a , b , c and p, q, r and the projection of the abc to pqr a - > p b - > q c - > r here known point values are a b c p q and r unknown. $\overline{PR}=\overline{AC}$ ...
1
vote
2answers
47 views

Problem about circle tangents [duplicate]

Circles $c_1$ and $c_2$ with origins $O_1$ and $O_2$ are on plane. $O_1Z$ and $O_1X$are tangents to Circle $c_2$.These tangents intersect $c_1$ in $A$ and $B$.$O_2Y$ and $O_2T$are tangents to ...
0
votes
2answers
24 views

Considering a convex polygon lying on a plane in 3D space, how can I know if a point on that plane lies inside or outside that polygon?

I have a plane in space and a polygon in it. I know the position of each vertices making the polygon. I also know the position of the point on the plane. How can I know whether the point is inside or ...
1
vote
3answers
258 views

Center of Mass in 3D object?

How would I find the center of mass in a 3D object (a "spinning top" or "dreidel") that consists of a cylinder welded on top of a box welded on top of an upside down cone? Assume building material is ...
0
votes
0answers
10 views

The area of a tangent Sweep to a space curve is equal to the area of its conical Ikon.

Can any one please explain to me what does the term Ikon refer to. The area of a tangent Sweep to a space curve is equal to the area of its conical Ikon.
0
votes
0answers
33 views

A question on relating $N$-Sphere with a $(N-1)$-cell in $\mathbb{R}^{N-1}$

Let there be a $N$-Sphere in $\mathbb{R}^N$. Every point in it is a unit vector in $\mathbb{R}^N$. Every real valued function $f$ defined on this sphere accepts a unit vector $\hat{a}\in\mathbb{R}^N$ ...
0
votes
0answers
18 views

ellipse and focus question

A whispering gallery is constructed as part of the surface formed on rotation of the ellipse x^2/100 + y^2/k = 1 with x and y in yards. Each whisperer stands at a focus on the x-axis that is three ...
0
votes
2answers
46 views

Is $\{\langle x,y\rangle\mid 1 \leq x \leq 2, y = 0\}$ compact in $\Bbb R^2$?

Is this set in $\Bbb R^2$ compact: $$\{\langle x,y\rangle\mid 1 \leq x \leq 2, y = 0\}$$ I think it is compact, but the answer says not. Any help is appreciated.
0
votes
2answers
21 views

Finding points in the same quadrant, when do I use polar coordinates?

Which two points of the following are in the same quadrant: $$(1,4),(e,-1),(2,\frac{\pi}{2}),(-3,-5),(-6.4,\frac{1}{3})$$ I am confused about this question, because it doesn't say anything about ...
1
vote
1answer
39 views

Find the ratio $PA:AT$

$PQRS$ is a parallelogram. We know that $T\in{QR}$, $\frac{QT}{TR}=\frac{3}{2}$ and that $A=PT\cap QS$. We have to find the ratio $\frac{PA}{AT}$. I know this is a primary level question, but I ...
1
vote
2answers
51 views

geometry - cross sections

https://imageshack.com/i/idJpH0gIj Here is a link to the picture I will be using. It said on here it was to big to upload. So with this picture I want to find/construct the cross section that ...
2
votes
1answer
49 views

How to mark rational points on a sphere

I found this picture on mathoverflow, which I find very intriguing and so I like to know how to draw such an image with a simple computer program. To calculate the rational point, I can draw a line ...
1
vote
1answer
32 views

A question on the rectangular region defined for a vector in $\mathbb{R}^N$

Let $K = (k_1,k_2,k_3,...k_N)$ be a vector in $\mathbb{R}^N$, consider the region $S_K$ consisting of all vectors $L = (l_1,l_2,l_3,...l_N)$ such that, $|l_i| \le |k_i| \forall i \in \{1,2,3,...N\}$. ...
1
vote
1answer
32 views

Can you graph equations with a negative discriminant? And how do you plot complex numbers both on a 2D complex plane and a 4D complex plane?

I don't understand the relationship between complex numbers and that way they are graphed. The equation I am working with is $2x^{2} - 6x + 5 = 0$ where my two roots are complex solutions: $x = ...
0
votes
0answers
30 views

What does this Perspective-projection matrix in 2D do?

Given a projection axis $X$, camera positioned in the origin and $d$ the distance to the projection plane, this is the perspective projection matrix: $$ P = \left[ \begin{array}{@{}ccc@{}} 1 & 0 ...
0
votes
1answer
29 views

cells of quotient CW complex

Let $X$ be a CW complex and $Y$ a CW subcomplex. If $X$ has no cell of dimension $n$, for some $n>0$, then $X/Y$ has no cell of dimension $n$. Is it true? Why?
0
votes
1answer
27 views

smash product of Eilenberg-Maclane spaces

Let $G$ be an abelian group and $K_n=K(G,n)$ be the Eilenberg-Maclane space. How to obtain $K_m\wedge K_n$ is $(m+n-1)$-connected? (Hatcher's book page 404)
0
votes
2answers
36 views

Is that possible that a inscribe angle can be greater than 90 degree

I have found a question like following: Its asked that what could be the angle x if BC is not diameter of the circle. So, my question is if it possible to be greater then 90 for an angle like x? ...
0
votes
0answers
35 views

Ellipse focus locus

What curvature properties ( intrinsic equation) does the locus of focus of an rolling ellipse on outside of a fixed circle have? (When circle becomes larger and flat, the locus tends to a constant ...
3
votes
2answers
51 views

The length of the smallest possible ladder to change the bulb.

In the drawing, the point P, a bit located under the bulb, has coordinates (a, b​​), where a and b are two parameters. You want to change the bulb, and for this it is necessary to install a ladder ...
1
vote
4answers
103 views

How to find the intersection point of two moving circles?

I'm trying to develop a simulation in C#, and I have to find the intersection (or collision) point of two moving circles, in 2D space. Actually one of my circles will be stationary, so only one of ...
5
votes
1answer
90 views

what is vector $(\vec{a}\cdot \vec{b})\vec{c} + (\vec{b}\cdot \vec{c})\vec{a} - (\vec{c} \cdot \vec{a})\vec{b}$

Suppose we have three non orthogonal vectors in $R^3$ as $\vec{a}, \vec{b}, \vec{c}$. The vector of $(\vec{b}\cdot \vec{c})\vec{a} - (\vec{c} \cdot \vec{a})\vec{b}$ is in the plane spanned by ...
4
votes
2answers
123 views

What is a geometric structure?

Every elementary book on abstract algebra usually begins with giving a definition of algebraic structures; generally speaking one or several functions on cartesian product of a point-set to the set. ...
2
votes
3answers
52 views

homotopy groups of wedge sum

Let $X_\alpha$ be connected CW-complexes. Then from Hatcher's book, $$\pi_{n}(\prod_{\alpha} X_{\alpha})=\prod_{\alpha}\pi_{n}(X_{\alpha}).$$ Is it true in general $$\pi_{n}(\bigvee_{\alpha} ...
0
votes
1answer
25 views

Area Of Polygon Whose Edges Are In Given Distance From A Given Polygon Edges

I'm handling a problem which I find quite difficult to solve; My input is a changing number of coordinates (real GPS coordinates), usually I get 4-8 coordinates, and another number,which indicates a ...
0
votes
1answer
25 views

Point on a sphere - translating reference axis

I have a point on unit sphere described by two angles : zr = Angle of rotation around the z-axis zi = Angle of inclination from the z-axis The problem that I have is that the data I need to use is ...
3
votes
1answer
38 views

Tiling squares with L-Trominoes

Is there a simple proof that any square besides a 3x3 square with area divisible by 3 is tileable with L-trominos?
0
votes
0answers
14 views

Geometry problem - lines/piece wise defined function

I am bothered by a certain problem. Suppose $x$ lines are drawn in the plane where no two of them are parallel and no three or more meet at one point. How many unbounded regions are there? Its pretty ...
3
votes
1answer
34 views

proof involving a triangle with a point inside it. [duplicate]

Suppose we have a triangle, call it triangle $XYZ$, and a point $W$ inside triangle $XYZ$. How would I prove that $XY + YZ > XW + WZ$? So the way I labeled everything, point $X$ is the bottom left ...
2
votes
1answer
35 views

Show that this construction is a parallelogram.

Let $ABC$ be a triangle. The middle of the segment $BC$ is denoted by $M$ and the centroid of $ABC$ is rated $G$. We construct $G'$ on the line $GM$ such that $|GM|=\frac{1}{2}|GG'|$ and ...
3
votes
2answers
117 views

Can one prove existence of incommensurables without the Pythagorean theorem?

Euclid's proof that the side and the diagonal of a square have no common measure, probably going back to Pythagoreans, reduces it to proving the irrationality of $\sqrt{2}$. This reduction uses the ...
1
vote
0answers
25 views

Distance of the plane relative to the base of a Pyramid.

Consider a pyramid is cut by a plane parallel to its base. Question: What is the distance of the plane relative to the base so that the volume of the truncated pyramid so formed is $\frac{3}{8}$ of ...
1
vote
2answers
59 views

Why must closest approach occur when relative velocity is perpendicular to motion?

The first part i) I can solve correctly, but I need some advice and intuition on how to solve the second part ii). Here is the mark-scheme for the question: But for part ii) I do not understand ...
0
votes
1answer
49 views

Circles and tangents and circumcircles

Question: Tangents drawn from the point $P(1, 8)$ to the circle $x^2 + y^2 -6x -4y -11=0$ touch the circle at the points $A$ and $B$. What is the equation of the circumcircle of the triangle $PAB$? I ...