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

1
vote
3answers
25 views

Use Vectors To Show Three Vertices Belong to a Right Triangle

The Full Question Theorems Used This is what I call theorem 1: My Work This problem has two major steps as far as I can see. First, I must show that these are points of a triangle(not ...
1
vote
2answers
26 views

Find the equation of line in new co-ordinate system.

A line is represented by equation $4x+5y=6$ in the co-ordinate system with the origin $(0,0)$.You are required to find the equation of the straight line perpendicular to this line that passes ...
0
votes
2answers
19 views

Construct a regular hexagon of specific height?

Is it possible to construct a hexagon of particular height, meaning distance between the faces (not vertices)? I have seen various methods of constructing a hexagon (ruler and compass only) which are ...
0
votes
1answer
10 views

Find the length of the intercept cut by the side $BC$ on the y-axis .

The equation of two equal sides $AB$ and $AC$ of isosceles triangle $\triangle ABC$ are $x+y=5$ and $7x-y=3$ respectively.What will be the length of the intercept cut by side $BC$ on the y-axis? ...
3
votes
0answers
23 views

Does every irreducible projective cubic curve have a nonsingular point of inflection?

Does every irreducible projective cubic curve necessarily have a nonsingular point of inflection? I've been trying to construct counterexamples, to no avail, which leads me to believe the question can ...
6
votes
1answer
60 views

Can eight circles be constructed from three circles?

Given three sufficiently spaced circles in a plane, is it possible, using a straight edge and compass, to construct the eight circles that are tangent to all three given circles?
-1
votes
1answer
25 views

The minimum perimeter and maximum height of a triangle under constraints [duplicate]

I do not get the following formulas : The minimum perimeter of any triangle (abc), given the heights corresponding to the a and b-sides. The maximum height corresponding to the side b of any ...
1
vote
1answer
27 views

Area Between Intersecting Lines - Elegant Solution?

I am running simulations, and the output will be a line y = mx+b. I am interested in the area below the line between x=0 and x=1. I am only interested in the area that is below the diagonal y = x. I ...
0
votes
0answers
14 views

Relationships Between Moduli Space and Objects They Parametrize

My friend and I were wondering recently what, if any, are the relationships between the geometric properties of a moduli space and the geometry of the objects that the space parametrizes. As an ...
2
votes
3answers
23 views

Gradient of a line

The line L is a reflection of the line $2y + 3x =9$ in the $y-$ axis (I had to draw the graph on the grid previously) Find gradient of the line L How would I go about solving this?
1
vote
2answers
20 views

Find the area of $\triangle POQ$ .

If $P$ and $Q$ are two points on the line $3x+4y=-15$ such that $OP=OQ=9$, then the area of $\triangle POQ$ will be ? $\color{green}{a.)18\sqrt2}\\ b.)3\sqrt2\\ c.)6\sqrt2\\ d.)15\sqrt2$ The ...
1
vote
0answers
4 views

Dinamically generate Goldberg polyhedra G(m,n)

In these pages the autor provided a lot of info about some Goldberg polyhedra (http://en.wikipedia.org/wiki/Goldberg_polyhedron): http://dmccooey.com/polyhedra/DualGeodesicIcosahedra.html ...
2
votes
3answers
58 views

Prove this is a rectangle

Suppose we have quadrilateral $ABCD$ where $m\angle A = m\angle B = 90^\circ$ and $AB \cong CD$. Is this figure always a rectangle? If not, can someone give a counterexample? I tried drawing the ...
2
votes
3answers
17 views

Find the relationship between $a$ and $b$.

If the medians $PT$ and $RS$ of a triangle with vertices $P(0,b),Q(0,0)\ \text{and}\ R(a,0)$ are perpendicular to each other,which of the following satisfies the relationship between $a$ and $b$? ...
5
votes
2answers
68 views

Geometric intuition for derivatives of basic trig functions

I was inspired by this question to try and come up with geometric proofs for the derivatives of basic trig functions--basically, those that have simple representations on the unit circle ($\sin, \cos, ...
0
votes
0answers
15 views

Determine the correct calculation to maintain visual exactness between two squares with different centers of rotation

I'm encountering this math problem while working on some CSS / JavaScript, so the coordinate system as well as dimensions are noted as such. I've been scratching my head at this for a while and ...
-1
votes
1answer
31 views

differntial geometry

i m facing much difficulty in understanding behaviour of acceleration vector relating to unit normal vector &unit tangent vector . However,study reveals that tangent vector is perpendiular to ...
-2
votes
2answers
28 views

Find the length of the diagonals? [on hold]

ABCD is a rectangle. It's diagonals meet at $O$. Find the length of the diagonals if $OA=3x+5$ and $OB=2x+9$.
-1
votes
0answers
7 views

How to calculate the horizontal offset of the top Bezier point of an Arc

Given the following: A circle with a diameter D 3 Bezier points P0 P1 and P2 that make an equilateral triangle, and the upper point P1 is at the top of the circle. The distance between P0 and P2 is ...
1
vote
1answer
17 views

Identification of the Lie algebra of an isotropy group with the tangent space - stuck with a statement

I think I am stuck with the following statement that I read on the Encyclopedia of Mathematics website regarding Isotropy representations: "If $G$ is a Lie group acting smoothly and transitively on ...
2
votes
2answers
28 views

Maximum perimeter for triangle inscribed in circle

How to prove that isosceles triangle has maximum perimeter from all trangles inscribed in circle? I found that from all isosceles trinagles - equilateral has maximum perimeter: Maximum perimeter of ...
5
votes
1answer
39 views

What does a linear equation with more than 2 variables represent?

A linear equation with 2 variables, say $Ax+By+C = 0$, represents a line on a plane but what does a linear equation with 3 variables $Ax+By+Dz+c=0$ represent? A line in space, or something else? On ...
1
vote
1answer
25 views

Finding the largest box inscribed in the ellipsoid

Among all rectangular boxes inscribed in the ellipsoid: $$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}=1$$ How to find the one with the largest volume?
2
votes
0answers
30 views

For points A, B, does there there a billiard such that any trajectory from A will reflect twice and then reach B?

I'm looking for a kind of generalisation of an ellipse; a shape with a more complicated optical property. I'm not sure how to rigorously define this shape, or prove that it exists, or find an equation ...
7
votes
1answer
46 views

Irreducible projective cubic, exists continuous surjection?

Let $C$ be an irreducible projective cubic in $\mathbb{P}_2$ with a singular point $p$. So consider $f: \mathbb{P}_1 \to C$ defined as follows. Identify $\mathbb{P}_1$ with the set of lines in ...
1
vote
2answers
29 views

Find the length of $2$ points based on intersection of a circle

Would anyone know the formula for finding the length of $BC$ giving the below data. $AB = 20$ $r = unknown$ $BC = ?$ The other dimensions that can be used if needed are written on the diagram. ...
3
votes
1answer
54 views

Necessarily a homeomorphism?

Let $D$ be the projective curve defined by $y^2z = x^3.$ Consider the map $f: \mathbb{P}_1 \to D$ defined by$$f[s, t] = [s^2t, s^3, t^3].$$Is it necessarily a homeomorphism? Any help would be greatly ...
2
votes
2answers
44 views

how many possible acute triangles with perimeter given

How many possible acute triangles exist with perimeter 18? All sides are positive integers. The triangle (7,7,4) is the same as (4,7,7). I need the work in a way that a geometry 9th grade student ...
2
votes
0answers
63 views

Geometric proof for Sophomore's dream

Is there a "visual proof" for sophomore's dream? $$\int_0^1 x^{-x}\,dx = \sum_{n=1}^\infty n^{-n}.$$ In the wikipedia article there are two algebraic proofs, but the integral and the summation has ...
1
vote
1answer
24 views

Find parametric line between two 2D line segments that is an exact distance from a point

Given two 2D line segments, $\overline{ab}$ and $\overline{cd}$, and a point $p$, I would like to find a scalar value $t$ such that the line segment between $\overline{ab}(t)$ and $\overline{cd}(t)$ ...
0
votes
0answers
42 views

The degree-genus formula cannot be applied to singular curves in $\mathbb{P}_2$?

(The degree-genus formula) The Euler number $\chi$ and genus $g$ of a nonsingular projective curve of degree $d$ in $\mathbb{P}_2$ are given by$$\chi = d(3-d)$$and$$g = {1\over2}(d-1)(d-2).$$ My ...
1
vote
1answer
21 views

Can a compact set of $\mathbb{R}$ have some properties and not being convex

The question is related to this one On a condition when bounded sets in R n is convex ?. Suppose that $n > 1 $ and that $C \subset \mathbb{R}^n$ is a compact (closed and bounded) set having a ...
1
vote
1answer
32 views

What will be the equation of side $BC$.

The equation of two equal sides $AB$ and $AC$ of an isosceles triangle $ABC$ are $x+y=5$ and $7x-y=3$ respectively . What will be the equation of the side $BC$ if the area of the triangle ...
8
votes
6answers
454 views

Finding the largest triangle inscribed in the unit circle

Among all triangles inscribed in the unit circle, how can the one with the largest area be found?
2
votes
2answers
36 views

The four straight lines given by the equation $12x^2+7xy-12y^2 =0$ and $12x^2+7xy-12y^2-x+7y-1=0$ lie along the side of the?

I know these equations are called general equation of second degree and also represent a pair of straight lines . I could extract lines from the equation $$12x^2+7xy-12y^2 =0 $$( these are $$ ...
3
votes
1answer
47 views

length of the curve $y=x^n$ in the unit square

Let $l_n$ be the length of the curve $y=x^n$ in $[0,1]\times[0,1]$. Then obviously $\lim_{n\to\infty}l_n = 2$. What about $\lim_{n\to\infty}(n(2-l_n))$ ? The formula $l_n = ...
-3
votes
1answer
46 views

How to do this triangle question? [on hold]

ADB is a straight line. Prove that AD = BC
4
votes
1answer
291 views

Prove this is an isosceles triangle

In a triangle ABC, $\sin B\cdot\sin C=\cos^2(\frac{A}{2})$ Prove that this is an isosceles triangle. Can anyone guide me to prove this? Thanks
3
votes
2answers
39 views

sum of perpendicular distances from the sides of a triangle.

I am trying to solve a problem and got stuck in the following:- P, A’, C’ are respectively points on the sides AC, CB, and AB of ⊿ABC. PA’ and PC’ are the perpendiculars to the sides of the ...
0
votes
1answer
29 views

Check if the following are perpendicular.

I have these expressions : $$2x+2y-5=0 \\ x=3-t,y=2+t,z=1-3t$$ I need to check if they are perpendicular. This is what I did : The following vectors represent the expressions $\langle ...
1
vote
2answers
13 views

How to find the vertex of a rhombus?

I am unable to solve this question. If the area of a rhombus is 10 sq.unit . It's diagonals intersect at (0,0) if one vertex of the rhombus is (3,4) , then one of the other vertices can be ? I took a ...
2
votes
1answer
71 views

Trirectangular tetrahedron

Looking at http://mathworld.wolfram.com/TrirectangularTetrahedron.html I wonder what the symmetry group of a trirectangular tetrahedron is?
4
votes
4answers
42 views

Are circles and lines in two-space one-dimensional?

Circles and lines are normally regarded as one-dimensional objects. However, when embedded in two-space, they require two coordinates $(x,y)$ to specify a point within them. Are they still considered ...
1
vote
0answers
41 views

Geometry of Curves

I found this question in question paper of Geometry of Curves and surfaces from Leeds University. Can anyone help me how I solve it.
0
votes
1answer
13 views

Sacle the distance of lattice points

I know that for a hexagonal lattice generated by (0,1) and ($\sqrt{3}/2$,1/2) (i.e., when the distance between lattice points is 1), the number of lattice points in a circle of given radius $r$ can be ...
3
votes
2answers
36 views

If $x-2y+4=0$ and $2x+y-5=0$ are the sides of isosceles triangle having area $10$ sq unit .Equation of third side is?

Okay, I know two sides of an isosceles triangle are equal . I have also taken out the intersection points of the lines given in the question . Other than this , I have no clue about how I will find ...
1
vote
3answers
19 views

Complex plane (Show that triangle is right-angled)

The points $O$,$P$ and $Q$ in the complex plane represent the complex numbers $0+0i$, $4+2i$ and $3-i$ respectively. Find the exact length of $PQ$ and hence, or otherwise, show that triangle $OPQ$ is ...
3
votes
6answers
101 views

Visualize $z+\frac{1}{z} \ge 2$

As we know, always $$z+\frac{1}{z} \ge 2,~~~~~~~~~ z\in \mathbb{R}^+$$ However, is there any geometric way to visualize this equation for some one who is not that expert in math? I know this ...
8
votes
5answers
182 views

Difficult Coordinate Geometry and Calculus Question

I was given this question by a friend and after tirelessly working on it I have not come up with anything substantial. I was hoping someone in the community could provide a pointer or possibly a ...
-1
votes
0answers
21 views

how t calculate the area of a rectangle intersected by an arc [on hold]

I need to make two calculations: Determine the arc that is needed between the two intersection points of a rectangle. Knows: Size of the rectangle, location of the intersection points. I want to ...