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

2
votes
1answer
50 views

Certain Geometry proofs seem not rigorous at all.

For example, this proof from Kiselev's "Planimetry": Theorem: The diameter (here, AB), perpendicular to a chord (here, CD), bisects the chord and each of the two arcs subtended by it. The proof: ...
1
vote
1answer
23 views

Area ratio in a parallelogram

Let $ABCD$ be a parallelogram, and let $M$ and $N$ be the midpoints of $BC$ and $CD$, respectively. Let $P$and $Q$ be the intersections of $BD$ with $AM$ and $AN$, respectively. Then find the ratio of ...
2
votes
2answers
26 views

Find the side of the pentagon

Let $ABCDE$ be a pentagon inscribed in a circle. Given that $AB=CD$, $BC=2AB$, $AE=1$, $BE=4$, $CE=8$. Find $DE$. I am unable to use the properties of circle in this question. All I could do was fund ...
0
votes
0answers
22 views

A homework question on geometry

This is a homework question: And the related definition is as follows: I know how to prove that $P_C(O)=-P_M(O)$ but have no idea how to proceed from there. Any hints will be appreciated.
0
votes
0answers
3 views

Conversion between quaternion and fixed axis

I have a set of quaternion angles for rotation of an object in 3D space: 0.2727 -0.8667 1.3774 0.8000 with associated Euler angles (deg) in XYZ order: 58.8 -10.9 125.9 May I know how could I ...
-5
votes
3answers
28 views

Geomety help, need help finding the answer [on hold]

Shane wants to put tiles in his bathroom. Each tile is a regular hexagon with a radius of 1 in. They need to cover an area that is 48 square ft. About how many tiles do they need? Round to the nearest ...
0
votes
0answers
17 views

Add lines between points in a Desmos graph [on hold]

I am currently making a desmos graphing calculator graph for a project. I have been able to create a table and rotate the figure represented by the table $a^\circ$ either clockwise or ...
0
votes
3answers
35 views

What is the plot of this function? [on hold]

What is the plot of this function? Suppose that a, b and r are constants. $$|x-a|+|y-b|=r$$
0
votes
0answers
22 views

How to formulate the critical density of balls in a cube to have a path from the upper surface to the lower one?

I want to approximately formulate the critical density of balls in a cube to make sure that the upper and lower surfaces of the cube will be connected to each other through these balls. So for ...
-3
votes
0answers
41 views

How do I prove that an ordered field and positive cone are bijective?

A field $K$ together with a binary relation $<$ is an ordered field provided the following hold: (O$0$) If $a \in K$, then one and only one of the following holds: $0<a$, $a=0$, or $a<0$. ...
3
votes
2answers
39 views

Finding angles plane geometry

$\Delta ABC$ is obtuse on $B$ with $\angle ABC = 90 + \frac{\angle BAC}2$ and we have a point $D \in AC$ (in the segment, I mean D is in between A and C) such that $\angle BDA = \angle ABD + ...
0
votes
2answers
39 views

What is the difference between the geometric and trigonometric definition of an angle?

I vaguely remember reading that there is a difference between the geometric definition of an angle and the trigonometric definition of an angle. I've tried to search everywhere I can think of but I ...
-1
votes
0answers
22 views

Question about the evolute of a plane curve

Let $\alpha$ be a plane curve $\alpha: I \rightarrow \mathbb{R}^{2}$. We consider its evolute $\beta$, whose parameterization in function of the arc of $\alpha$ is :$$\beta(s) = \alpha(s) + ...
0
votes
1answer
17 views

Find longer side of a rectangle with respect to another rectangle

So I have two rectangles: Rectangle R1 with width r1w and height r1h Rectangle R2 with width r2w and height r2h I can find the slope/aspect ratio of the two ...
1
vote
2answers
31 views

Circles question on proof

It is given that a, b, and c are the sides of a triangle and c is the hypotenuse. There is an incircle inside the triangle with radius = r. We need to prove that $r=\dfrac{a+b-c}{2}$ Image: My ...
0
votes
0answers
13 views

Term for similarity transformation which is not a translation

What's the best (i.e. most concise) term to refer to an orientation-preserving similarity transformation which is not a translation? Here are some descriptions I could think of, but all of them feel ...
1
vote
1answer
35 views

Does every shape have zero volume?

Consider the digram below: the red line ($c$) enclosing an area on the XY plane lies in the yz plane and the blue line is a surface with this line as its boundry curve. Let's say we are trying to ...
0
votes
1answer
25 views

In how many ways can the rooks be arranged? [duplicate]

In how many ways can 9 black and 9 white rooks be placed on a 6 × 6 chess board, so that no white rook can capture a black one? A rook can capture another piece if it is in the same rank (row) ...
2
votes
2answers
27 views

Help in making an animated locus is needed

I have triangular cardboard ABC, right angled at C. As shown in the attached, initially, A and B are resting on the x- and y- axes respectively. A is then allowed to slide along the x-axis with B ...
0
votes
0answers
42 views

Is there a real world application for the Poincaré Conjecture? [duplicate]

As the title asks, is there currently a way in which the conjecture, or proof, can be implemented in a real world way?
2
votes
1answer
43 views

Geometrical Combinatorics About Rectangles

Part of a olympiad problem The answer is $$441 = 21^2$$ I fail to understand why. How do you solve this? I actually dont see why there are $9$ rectangles there either? Can someone give me a hand?
0
votes
2answers
18 views

Bearing of a line or a point

Rochelle is 25 miles due south of Rockford,and North Chicago is 65 miles due east of Rockford.Find the bearing of North Chicago From Rochelle. I used Pythagorean theorem in solving this because i ...
0
votes
0answers
13 views

Curve traced by following a Jordan curve.

Let $C$ be a Jordan curve in the plane and fix a point $x$ on $C$. For a point $v$ on $C$, define the curve $C_{v_a}$ as follows: draw a line from $x$ to $v$ and two additional lines to a point $a$ so ...
3
votes
4answers
44 views

Limit of ratio of areas of triangles defined by tangents to a circle

Let $AB $ be an arc of a circle. Tangents are drawn at $A $ and $B $ to meet at $C $. Let $M $ be the midpoint of arc $AB $. Tangent drawn at $M $ meet $AC $ and $BC $ at $D $, $E $ respectively. ...
0
votes
1answer
16 views

Point in a triangle plane determining any angles

Let $\triangle{ABC}$ be an arbitrary triangle. Is it true that for any angles $\alpha, \beta,\gamma\in [0,2\pi]$ with $\alpha+\beta+\gamma=2\pi$ one can find a point $M$ in the plane of the triangle ...
2
votes
2answers
69 views

Geometric proof of $\frac{\sin{60^\circ}}{\sin{40^\circ}}=4\sin{20^\circ}\sin{80^\circ}$

It is well-known that $$\sin{20^\circ}\sin{40^\circ}\sin{80^\circ}=\frac{\sqrt{3}}{8}$$ It follows that $$\frac{\sin{60^\circ}}{\sin{40^\circ}}=4\sin{20^\circ}\sin{80^\circ}$$ But how to prove this by ...
0
votes
1answer
24 views

Complement and supplement angles

This High school Honors geometry question got my eyes turn around my head, in part of the language involved. It goes like: "The supplement of an angle is 60 degrees less than twice the supplement of ...
0
votes
0answers
18 views

How to formalize the subjective perception of perspective?

Suppose you're moving in a car or a train in the direction of the $x$ axis with some velocity with respect to the ground. If you look through the window (that is, at the $y$ or $z$ axis), what you ...
2
votes
2answers
16 views

Trying to find function that defines a parabolic surface

Say we are working in three dimensions and we have a function $u_1(x, y) = x^2$. Ie. this is just the regular $x^2$ parabola except it's now defined all along the way $y$-axis and forms a surface. ...
0
votes
1answer
26 views

Finding the slope at a given point on the intersection of a surface and a plane

The surface with equation $z = x^{3}+xy^{2}$ intersects the plane with equation $2x−2y = 1$ in a curve. What is the slope of that curve when $x = 1$ and $y = -\frac{1}{2}$? I'm a little confused ...
-2
votes
1answer
29 views

What is the volume of the juice in the given glass? [on hold]

The radius of the upper part $r_1$ and lower part $r_2$ is given. If height of the glass is $h$ and height of the juice is $p$ ($h$ and $p$ given) what is the volume of the juice in the glass?
0
votes
1answer
15 views

What is the probability of a circle sector being chosen at random?

What should I do in order to find the probability of the sector? Can you please give me the answer to this. It will really help me out if you do.
-1
votes
5answers
33 views

How do I find the area of this shaded circle?

This circle has been bugging me for a while, and I do not know how to solve it. Can someone help me find the area of the shaded circle? It would really help me.
0
votes
1answer
30 views

How to explain that this line is perpendicular to this one?

I have got this figure : It is obvious that (FK) is perpendicular to (IJ), but I can't explain, with a simple sentence, why it is like this... Thank you.
0
votes
0answers
46 views

pure and applied math [on hold]

is there a connection between pure math and other sciences like biology ? I mean that I like this part of pure math that definitions and theorem are exactly applied to the other sciences (if it ...
1
vote
2answers
37 views

Problem in proving that the locus of all points S is a circle.

Given is a circle with midpoint $M$ and a chord $AB$ on this circle. $S$ is the intersection of the altitude from $M$ to $AB$. Prove that the locus of all points $S$ is a circle with midpoint $D$ ...
0
votes
2answers
26 views

Proof of Alternate, Corresponding and Co-interior Angles

During school our teacher always explains the proof for all theorems even simple ones such as why does the angles in a triangle of add up to $180$ and they all involve alternate, corresponding or ...
0
votes
2answers
30 views

Proving that two lines are not from the same plane?

Well, I'm looking for a clean but effective way to prove that two lines in the space are or are not from the same plane, knowing that these two lines are given by their parametric representations.
0
votes
1answer
25 views

differential perimeter of an ellipse

If I define an ellipse in polar system of $r$ and $\phi$ as shown in figure below, what is the length of differential element $(ds)$ on its perimeter in polar coordinate system? Note: Please be ...
-2
votes
0answers
40 views

Cow Grazing Word Problem [on hold]

http://imgur.com/sOj66jk Consider the values of X = 17.987 and X = 17.241. What is significant about these values? How does this affect the general expression for grazing area of X < 3, 3 < X ...
1
vote
1answer
18 views

Area of a trapezoid given the areas of triangles A and B whose bases are the parallel sides of the trapezoid

So for example if we have trapezoid ABCD then we could draw diagonal BD and AC. They would intersect at a point and create four triangles. So say that we knew the area of the two triangles whose bases ...
0
votes
0answers
31 views

the fibonacci circle section Just One? [on hold]

I can find only one circle section in which all four of it's straight measures are Fibonacci numbers. Is it the only possibility or are there more?
1
vote
2answers
31 views

Question involving area and perimeter of two parallelograms sharing a diagonal.

Given two parallelograms $P1$ and $P2$, such that area of $P1$ is greater than area of $P2$, can we say that the perimeter of $P1$ is greater than the perimeter of $P2$ ? Actually I was trying to ...
0
votes
0answers
17 views

finding the polar set

the question say find the polar-duals of the following sets in $R^2$ 1) {(x,y):x>=2} 2) {(x,y):x<=2} 3) {(x,y):x=2} the answers are {(x,0):x<=0} , {(x,0):0<=x<=1/2} , {(x,0):x<=1/2} ...
4
votes
2answers
214 views

How can one find the area of the blue shaded region?

Here 3 circles are touching each other. Now how can one find the area of the blue shaded region in the given picture?
10
votes
3answers
100 views

How to prove $x=120^\circ$

Let $ABC$ and $CDE$ be equilateral triangles. How to prove that $x=120^\circ$? Thank you.
-2
votes
1answer
31 views

Find the equation of two circles , geometry [on hold]

Find the equation of the two circles tangent to the line $x+y+4=0$ and $7 x-y+4=0$ .. and having their centers on the line $4x+3y-2=0$.
0
votes
0answers
19 views

About finding a binary relation

Let $δ_{n},β_{n}$ two sequences of rational numbers. Assume that the points $$P_{p}=(δ_{p-1},β_{p-1})$$ $$Q_{p}=(δ_{p},β_{p})$$ $$R_{p}=(δ_{p+1},β_{p+1})$$ are colinear and assume also that the ...
1
vote
2answers
25 views

Ratio of parts of a triangle

In the diagram above, segment DE is parallel to segment BC and the ratio of the area of triangle AED to the area of trapezoid EDBC is 1:2. How can I find the ratio of AE to AC? So far, I got the ...
3
votes
3answers
64 views

Proof of a geometric statement

If $D$ is a point inside a triangle $\triangle ABC$ then how the following statement is true. statement: $AB+AC>BD+DC$. I have tried in the following way but it seems to me defective. ...