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
25 views

Construction of a triangle given some special points

I'm a newbie in this site. I tried to search if this question was already answered but I'm not sure on how to do it. The problem is: given three distincts points $O,H,I$ namely the circumcenter, the ...
0
votes
0answers
8 views

Finding a plane where a vector lies (and generating its normal)

I have a vector in homogeneous coordinates $l = (a,b,1)$ and want to calculate a plane from it (for later doing intersections in 3D coordinates and calculate collision coordinates) with regards to the ...
1
vote
1answer
12 views

I don't understand this from my lecture note. What is described by $x=X(\xi)$? Why $\xi(t)$ is a curve since $\xi \in R^{m-1}$?

I don't understand this from my lecture note. What is described by $x=X(\xi)$? Why $\xi(t)$ is a curve since $\xi \in R^{m-1}$?
0
votes
0answers
21 views

Geometric proof concerning circles

From a point P outside a circle draw two tangents to the circle touching at points A and B. draw a secant line intersecting the circle at points C and D. choose point Q on chord CD such that angle DAQ ...
1
vote
2answers
39 views

Triangle in parabola

I have a problem. In my triangle one vertex is in the vertex of the parabola and two others are in parabola. This is a isosceles triangle and I know one angle in this triangle : 120 grades. The ...
0
votes
0answers
8 views

Difference in (the concept of the distance between a line and a point) between Euclidean and non-Euclidean Geometry

What is the difference in (the concept of the distance between a line and a point on a graph) between Euclidean and non-Euclidean Geometry. Is this concept the same in all kinds of geometry??
1
vote
2answers
23 views

Can ellipse equation be transformed through one of its foci?

Can we transform ellipse equation to represent an ellipse transformed by tilting it through its focus such that its center point moves in circular manner and one of its focus stays at constant ...
2
votes
1answer
35 views

Weil divisors fail over singular varieties

Let be $k$ an algebraically closed field. We know that if $X$ is an irreducibile, normal variety, one can associate to every rational function $(f)\in k(X)^*$ a Weil principal divisor $$(f)=\sum_{Y} ...
1
vote
0answers
66 views

Crossed Ladders Problem

Two ladders, one 10 meters long and the other 8 meters [long], have been placed in a trench as indicated in the opposite figure. Their point of intersection, M, is 3 meters from the base of the ...
0
votes
0answers
9 views

Rational representation of conics

Currently I'm beginning my study of rational curves (Rational Bezier and NURBS) all books that I've read tell me that is "well known" that conics can't be represented by Bezier or even a B-Spline. ...
1
vote
2answers
23 views

How can I use Menelaus' theorem here (Simson line)?

Given 4 points on a circle A, B, C, and P. Draw the orthogonal projections of P onto triangle ABC and call them $P_1, P_2,P_3$. Show that $P_1, P_2,P_3$ are collinear. After drawing this out, I ...
1
vote
1answer
11 views

Proving that $2$-D parabolic coordinates are orthogonal

How can we prove that the parabolic coordinate system in two dimensions is orthogonal? I tried using the dot product, but don't know where to start or what basis vectors can be used in two dimensions. ...
0
votes
1answer
34 views

How would I use vectors for this geometry problem?

Consider a quadrilateral ABCD. K, L, M, N are the midpoints of the segments AB, BC, CD, DA respectively. O is the intersection point of LN, KM. Let P and Q be the middle points of the diagonals AC ...
1
vote
2answers
38 views

Trisecting the sides of a triangle.

Consider the hexagon formed by the six points which trisect the sides of a triangle(two on each side). Is is true that when we connect opposite points in this hexagon, the lines intersect at a single ...
2
votes
2answers
53 views

Distance between four points

I have four points as shown in this figure: I want to calculate one vector for all these points. So, what would be the correct way: 1) I take the vector between $A-B, B-C, C-D$ and add them $(A-B ...
4
votes
1answer
28 views

Is there a name for this special, “most parallel” ultraparallel line in hyperbolic geometry?

Suppose you're in the hyperbolic plane, and you have a line L and a point P not through L. There are an infinite number of lines parallel to L that go through P. However, there's one line M which is ...
2
votes
6answers
404 views

Is it possible to find the area of a shape from its perimeter?

Is it possible to find the area of a free form shape knowing the perimeter? An example would be a clover leaf shape. If the perimeter is 96 how would I know what the area would be?
0
votes
0answers
23 views

a valuable question about differential geometry, the curve$\beta(s)=\alpha(s)-rn(s)$

Let $\alpha(s)$,s$\in [0,l]$ be a closed convex plane curve positively oriented. The curve $$\beta(s)=\alpha(s)-rn(s)$$,where r is a positive constant and n is the normal vector, is called a parallel ...
1
vote
0answers
36 views

27 Lines on a Cubic

In Ravi Vakil's notes, there is a proof (in section 27, of course) of the famous result that every nonsingular cubic hypersurface in $\mathbb{P}^3_k$ over an algebraically closed field $k$ has exactly ...
0
votes
0answers
17 views

Intercept planet following an elliptical path (i.e. interplanetary space travel)

So, just as in this question (Intercept path to object following an elliptical path) I have a simple game where I want spaceships to intercept planets, which follow elliptical paths (in my case ...
-5
votes
3answers
37 views

The lines with equations $y = 5x − 6$ and $10x + cy = 8$ are perpendicular, find c [on hold]

The lines with equations $y = 5x − 6$ and $10x + cy = 8$ are perpendicular. Find the value of c. Well, I am not sure even where to start
1
vote
1answer
55 views

How can I find the common axis of 2 cones in space that have the same base radius but different heights?

How do I find the 3D vector describing the axis of 2 overlapping cones, like this: If I have only the following information: Coordinates of the common tip Coordinates of a point on the yellow ...
1
vote
0answers
10 views

Showing there is a cartesian coordinate system on EG.

I'm pretty sure I should just show there is a bijection between the points in EG and elements of R^2. How do I do this? note: EG=Euclidean Geometry
1
vote
0answers
19 views

Questions on curvilinear asymptotes

I just saw curvilinear asymptote which sort of fascinated me. A little bit of thinking raised two questions for which I couldn't get the the answer by googling. Is there a general method to find a ...
0
votes
1answer
22 views

Line between points in projective space?

I am trying to find the line through the points $(0 : 1 : 0)$ and $(1 : 1 : 1)$ in $\mathbb P^2$ and $(0 :1 : 0: 1)$ and $(1: 1: 1: 0)$ in $\mathbb P^3.$ Would the first line be the set of points ...
-1
votes
1answer
36 views

Formula to calculate angle on a fan or semicircle

How do I calculate the angle shown in the picture given the height, width, and the arc deduction of $2$? I had applied the Right Triangles formula to calculate the hypotenuse: $h^2 = a^2 + ...
0
votes
1answer
11 views

find a point such that the distance between this point and a plane is equal to the distance between another point and a line [on hold]

I have: $r:(2,1,0)+\lambda(0,4,-3) \qquad \pi:4y-3z-4=0 \qquad A=(2,4,4)$. I have to find a point $C$ such that $d(C,\pi)=d(A,r)$ where $d$ is the distance
0
votes
0answers
7 views

Can Magnification/Scaling (transformation) be prepresented by a vector?

Vectors represent three bits of information: Magnitude, Line of Action, and Direction. A Translation (transformation) can be represented by a vector: object is moved By so much (magnitude) Along a ...
0
votes
0answers
15 views

Parametric equations for hypocycloid and epicycloid

Suppose that the small circle rolls inside the larger circle and that the point $P$ we follow lies on the circumference of the small circle. If the initial configuration is such that $P$ is at ...
1
vote
0answers
14 views

For each point on a line there exists a unique perpendicular line through that point

I'm trying to show that in an absolute plane (only the first four axioms without the parallel axiom hold) for each Point $P\in l$ there exists exactly one perpendicular line through $P$. My idea was ...
2
votes
1answer
11 views

Given a number of vertices , a radius, and rotation calculate vertices' coordinates for regular polygons

So, I know half the answer to this but I don't know how to adjust it for rotation. I believe formula the below is correct if I did not have to take into account rotation. $r \cos(2 \pi i / n) = y$ ...
0
votes
0answers
15 views

Point on ellipse after walking a distance on the perimeter [duplicate]

I've the equation of an ellipse. Given a point (x,y) on the ellipse and a length L , I want to find the coordinates (x1,y1) of the point where I'd end up after taking a walk of length L from (x,y), ...
1
vote
0answers
19 views

Find Formal Proof on Loci Theorems

Please help me to prove this theorems of loci Theorem 12 The locus of a point at a given distance from a given line is two lines parallel to the given line and at the given distance from it. Theorem ...
0
votes
0answers
8 views

$\frac{4}{3}(1,-1,0)^T+\textrm{vect} \left((-1,1,-1)^T\right)$

Here I have a passage on the conclusion, but I do not understand it. the conclusion say : $f$ is the oriented axis of screw.. how I can from $\frac{4}{3} \begin{pmatrix}1\\1\\0 ...
7
votes
0answers
50 views

Can ${n \choose 2}$ points be covered by lines determined by $n$ points?

Let $S=\{(a_1,b_1),\ldots,(a_{n \choose 2},b_{n \choose 2})\}$ be ${n \choose 2}$ points on the plane. Does there exist $n$ points, such that the lines determined by the $n$ points cover all the ...
1
vote
0answers
8 views

union of two Geodesics

Let $X$ be a metric space. $a,b,c \in X$ and $\sigma_1 , \sigma_2$ geodesics from $a$ to $b$. Let $\sigma$ geodesic from $b$ to $c$. Want to show : $\sigma_1 \cup \sigma $ geodesic $\Rightarrow ...
0
votes
1answer
19 views

Length of tendon in circle [on hold]

What is the length of chord that pass on two specific point. For example I have circle ( r=1) point1 :(x1,y1) point2(x2,y2); length of chord?
0
votes
0answers
20 views

a question about differential geometry, the relation between osculating plane and the points of $\alpha(s)$

question:please prove the limit position of the circle passing through $\alpha(s)$,$\alpha(s+h_{1})$,$\alpha(s+h_{2})$ when $h_{1}$ and $h_{2}$ approaches 0 is a circle in the osculating plane at s, ...
0
votes
0answers
13 views

Is kahler geometry related to finsler geometry? [on hold]

Is kahler geometry related to finsler geometry? Is the metric $\partial_a\phi\partial_b\phi$ always kahler?
1
vote
2answers
44 views

If a curve $\gamma$ through two points $P,Q$ satisfy $\|Q-P\| = \int^{t_1}_{t_0} \| \gamma^{'} \| \, \text {d}t$, then $\gamma$ is a straight line?

In a theorem called "A straight line is the shortest curve through two given points", I prove that for any two points $P,Q \in \mathbb R^2$ and any curve $\gamma : (a,b) \rightarrow \mathbb R^2$ with ...
3
votes
1answer
43 views

Average distance to a random point in a rectangle from an arbitrary point

I'm interested in the mean distance between an arbitrary 2D point, $(p, q)$, and a uniformly distributed point inside a rectangle defined by the lower left and upper right vertices $(x_0, y_0)$ and ...
0
votes
1answer
33 views

Trying to define a simple “warp” function

I'm trying to define a 2D "warp" function y=f(x,w). A picture is worth a thousand bytes: I am looking for a simple function f(x, w) that satisfies the ...
1
vote
2answers
14 views

Geometry: What is the height of a solid pyramid

So the question is OPQRS is a right pyramid whose base is a square of sides 12 cm each. Given that the the slant height of the pyramid is 15cm. And now I need to find the Height of the pyramid. I ...
-8
votes
0answers
60 views

Prove that.. Please quick. [on hold]

If the length of perpendicular from the point $(1,1)$ to the line $ax-by+c=0$ be $1$, show that $1/c+1/a-1/b=c/2ab$. if $p$ and $p'$ be the length of the perpendiculars from the origin upon the ...
2
votes
0answers
27 views

Unique perpendicular line

Consider an absolute plane (i.e. it satisfies all axioms except the parallel axiom). Let g be a straight line and P a point not in g. Then there is a unique straight line going through P which is ...
0
votes
1answer
13 views

Inscribed Rhombus

Can a rhombus that is NOT a square be inscribed in a circle? A quadrilaterals opposite angles must add up to 180 in order to be inscribed in a circle, but a rhombuses opposite angles are equal and do ...
1
vote
1answer
23 views

Prove that there is exactly one perpendicular line

Consider an absolute plane (i.e. it satisfies all axioms except the parallel axiom). Let $g$ be a straight line and $P$ a point not in $g$. Then there is a unique straight line going through $P$ which ...
0
votes
0answers
6 views

Calculating the position of the ascending and descending nodes in an orbit

I'm working on a space sim and I'm stuck getting the position of the Ascending and Descending orbital nodes. I know how to get the position at any angle of the orbit, but it's measured from the ...
2
votes
1answer
18 views

Proof: number of intersection points of borders of a convex polygon and its translate never greater than 2

How can I prove the observation that the borders of a convex polygon $P$ with no parallel sides in $\mathbb{R}^2$ and a translate of $P$ by any vector $t\neq 0 \in \mathbb{R}^2$ that is not parallel ...
2
votes
2answers
31 views

When the intersection between a sphere and a cylinder is planar?

We have a sphere and a circular cylinder. Let the sphere center be $O$ and radius $R$, and the cylinder axis $a$ and radius $r$. I solved the specific case intersection graphically on 2 planar ...