For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, angles.

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0answers
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krull dimension of a direct limit of commutative rings

What can be said about the Krull dimension of a direct limit of non noetherian rings commutative rings with unit with constant Krull dimension?
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0answers
27 views

Zeros of vectorial field [on hold]

If $M$ is a manifold in ${\mathbb R}^n$ and $X:M\rightarrow TM$ a vectorial field such that $\pi\circ X=Id$ where $\pi:TM\rightarrow M$ (projection to $M$). One zero of $X$ is such that $X(x)=(x,0)$. ...
7
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5answers
210 views

Calculate this area without using integral?

Is there anyway to calculate this area without using integral ?
9
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2answers
133 views

Difficult Recurrence

I am trying to solve a Sangaku problem. The blue circles have radii one. The goal is to find the total area of all the other circles. I have almost solved the problem. I have found the area of ...
3
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0answers
18 views

Geometric meaning of a matrix decomposed into its symmetric and skew-symmetric parts

What's the geometric meaning of a matrix decomposed into its symmetric and skew-symmetric parts? For example, a skew-symmetric matrix on its own can be interpreted as an infinitesimal rotation. As ...
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1answer
23 views

A bounded domain can be considered as a compact manifold?

A bounded domain $\Omega$ with smooth boundary $\Gamma$ can be considered as a compact connect Riemannian manifold?
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1answer
26 views

Finding equation of line with given slope

Find the distances of the point (1,2) from a straight line. The slope is given to be 5 and the line passes through the intersection point of the lines $x+2y = 5$ and $x - 3y = 7$ Obviously I could ...
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1answer
12 views

Triangle Theorem relating the shortest and longest distance from any arbitrary point inside

I recall somewhere there was a relationship such that given a triangle T and a point A: if A is inside of T, then the sum of the longest distance from A to any point on a side of T, plus the shortest ...
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1answer
18 views

Why does a 3d line of segments with constant angles always make a helix?

I have a chain of discrete segments, of equal sizes, built by the following rules: 1)every next segment rotates around it's Y axis by 7 degrees, 2)then it pivots at the join with the previous ...
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1answer
25 views

Lines In the Complex Proyective Plane

The question is In how many points a line in CP^n intersects CP^2?. By a line in CP, I mean a copy from CP^1. I have tried with a sytem of equations, (Because a line in CP^n is the zero locus of a ...
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4answers
41 views

Smallest and largest possible angles of given polygon

What is the smallest and largest possible angle of a triangle? (my guess = 1, 178) What is the smallest and largest possible angle of a quadrilateral (convex or concave doesn't matter, and also ...
4
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0answers
33 views

How to integrate scalar field over quarter torus? Infinite series does not converge.

This seems to be physics question, but the problem just concerns math. Preface If one wants to calculate the permeance $P$ of a rectangular bar: it is an easy task: $$P = \frac{\mu a b}{L} ...
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3answers
65 views

Expected area of a random triangle with fixed perimeter

I'm trying to calculate the expected area of a random triangle with a fixed perimeter of 1. My initial plan was to create an ellipse where one point on the ellipse is moved around and the triangle ...
1
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2answers
34 views

Geometry : find the points of tangency between two lines and two circles [on hold]

I have a programming problem. I need to find the intersection points between two lines tangent to two circles and the circles! I have the circles' radiuses and centers. So I need points ...
0
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1answer
9 views

Retrieve the initial cubic bezier curve subdivided in two bezier curves

I have a cubic Bezier curve subdivided to two cubic Bezier: Assuming that "t_cut" is the t value where this initial Bezier is cut: example of function subdivision(BezierCurve initialCurve, ...
2
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0answers
42 views

How prove $\sum_{cyc}\sqrt{PA+PB}\ge 2\sqrt{\sum_{cyc}h_{a}}$

Question: let $\Delta ABC$,and the altitude is $h_{a},h_{b},h_{c}$,where $AB=c,BC=a,AC=b$ and for any $P$ show that $$\sqrt{PA+PB}+\sqrt{PB+PC}+\sqrt{PA+PC}\ge 2\sqrt{h_{a}+h_{b}+h_{c}}$$ ...
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2answers
60 views

Can anyone prove that this is an envelope of a parabola?

Based on my last question I learned that this is an envelope of a parabola What is this geometric pattern called? But how can I prove it ?
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1answer
27 views

How do I rotate a rectangle of latitude and longitude?

I have a rectangle with its corners specified in latitude and longitude. I would like to rotate it about it's centre a certain number of degrees. I was using longitude as an x value and latitude as a ...
8
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8answers
1k views

Polygons with equal area and perimeter but different number of sides?

Let's say we have two polygons with different numbers of sides. They can be any sort of shape, but they have to have the same area, and perimeter. There could be such possibilities, but can someone ...
2
votes
3answers
165 views

Is there any theorem about figures of equal area and perimeter being congruent?

I had an idea, that all geometric objects, that are different, as they're not a translation, rotation, and a reflection of one another cannot have the same area AND perimeter, as compared to ONE ...
2
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1answer
20 views

finding parallel sides from a irregular decagon?

Is it possible to find out that which of two sides are parallel in this irregular decagon.If,it is yes;then how can I proceed? I have tried with "Consecutive Interior Angles".but can't come to a ...
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1answer
35 views

Area of triangle/polygon

please see following picture: I am trying to find total area, so far- I was able to determine area of the semi-circles but I cannot figure out the area of the triangle in the middle. The variables ...
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1answer
16 views

Areas of tetrahedron surfaces - how to calculate?

Reading up on Cauchy's stress theorem, I have stumbled over the so-called Cauchy tetrahedron, which is an important part of the theorem's proof. The following is cited straight from Wikipedia, but a ...
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1answer
35 views

Keeping the arc length constant between points in a spiral

I'm making a visualization of points in a logarithmic spiral and want to keep the arc length between points (image particles) constant. I read that in an Archemedian spiral arc length is ...
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1answer
28 views

problem about Circumscribed circle of triangle

Qeustion circle O is Circumscribed circle of triangle $ABC$,where diameter $DE$ is perpendicular to segment $BC$ and intersects it in point $M$.perpendicular line from point $A$ to segment $DE$ ...
3
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3answers
78 views

How find $x$ in a right triangle $ABC$ (${\angle}A=90^\circ$) where ${\angle}DBC={\angle}DCA=x$,${\angle}BAD=5x$?

In a right triangle $ABC$ (${\angle}A=90^\circ$) taken in point $D$ such that $BD=AC$, ${\angle}DBC={\angle}DCA=x$,${\angle}BAD=5x$. How find $x$?
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0answers
29 views

Geometry Altitudes Triangles [on hold]

Points $D$, $E$, and $F$ are the midpoints of sides $BC$, $CA$, and $AB$ of $ABC$, respectively, and $CZ$ is an altitude of the triangle. If $\angle BAC=71$, $\angle ABC=39$, and $\angle BCA=70$, ...
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1answer
31 views

Medians Help (Triangles)

Medians line segment AX and BY of triangle ABC are perpendicular at point G. Prove that AB is equal to line segment CG. I'm working on this problem (I've already drawn a diagram) and I'm stuck, any ...
3
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2answers
54 views

Calculation for the chance of finding something a given distance from a starting point by walking straight in a random direction?

The premise is basically a 2D plane with a single point, the starting point. Now a landmark sought by a hiker is a certain distance from that point. If the hiker can only see 1 mile in any ...
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3answers
101 views

Strange proof of Schwarz Inequality with Pythagorean Theorem

Does anyone know what is going on in this proof of the Schwarz inequality? Most importantly: how can one assume that $c^2\leqq \|A\|^2$, or later on, that $c^2\|B\| \leqq \|A\|^2$? This would imply ...
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1answer
21 views

Logarithmic spiral appears inverted

I'm learning to code the equation for a logarithmic spiral for a graphics visualization. However, it appears to be inverted with the radius getting smaller (rather than larger) toward the outside of ...
3
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1answer
36 views

Geometries (Euclidean and Projective)

We can think of Euclidean Geometry and Cartesian (Coordinate) Geometry as equivalent, in the sense that some proposition is true in Euclidean Geometry iff it's true in Coordinate Geometry. It makes ...
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2answers
46 views

Find radius and height

I have the following problem: given the length of the chord AB and the length of the arc AB, find the radius of the circle and the height of the triangle ACB where C is a point on the circle such that ...
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1answer
32 views

Granted I have NE and SW coordinates for a rectangle, how do I get the center point?

I've got the NE and SW coordinates/points for a minimum bounding rectangle. How do I calculate the center point of this rectangle? At first thought, I could calculate this using simple division. ...
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0answers
19 views

Calculate distance between two objects based on their visible height for a specific focal length

How do I calculate the distance between to objects of the same size base on their height for a given focal length. Both object 1 and object 2 are 15 cm in height (actual size). Object 2 looks ...
1
vote
1answer
42 views

Is it possible to create a bigger square using distinct smaller ones?

Another user just inquired about possible solutions to the famous $70$x$70$ square puzzle. When I encountered that many years ago and the first idea that came to my mind as to why I wouldn't think it ...
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4answers
46 views

simple geometry question- equation of cylinder

A cylinder is $(x-a)^2+(y-a)^2=r^2$ with axis at $z$. I don't see where the '$z$' is in the equation. The book (calc 3) I'm using mentions the equation works for any $z$, but I don't see where the $z$ ...
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0answers
14 views

hexagon analogues of parallelograms

Is there a name for those hexagons whose opposite sides are equal and parallel and are there any interesting results about them in elementary plane geometry?
3
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2answers
45 views

Drawing a triangle from medians

Is it possible to draw a triangle, if the length of its medians $(m_1, m_2, m_3)$ are given only? Someone asked me this question, but I can not see it. Is it really possible? UPDATE Apart from the ...
5
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2answers
80 views

Can a convex polygon inside a square with edge length 1 have a perimeter > 4?

While featherbrainedly doodling the other day I noticed that it's probably impossible to draw a convex polygon with a greater perimeter then that of the square around it. Can someone find a ...
1
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0answers
48 views

A Homeomorphism that is not unique even upto Isotopy

I'm currently reading the following paper by Richard Skora, entitled Cantor sets in $S^3$ with simply connected complements found here, and on page 2, just before Theorem 1, it says "the homeomorphism ...
2
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1answer
32 views

How to embed this circle tangent to the other circles?

I want to construct a circle that would be tangent to the $3$ circles and would have its diameter lie somewhere on the segment $BI$. $EF$ includes the diameters of the $3$ given circles. $EB=BF$. ...
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1answer
64 views

Blow-Up over a Field

I want to prove that a function $\pi : \mathbb{C}_{*}^{n}\mapsto \mathbb{C}^{n}$ is bijective. Where $\mathbb{C}_{*}^{n}$ is the explosion of $\mathbb{C}^{n}$ and is defined as $\mathbb{C}_{*}^{n}:= ...
0
votes
1answer
23 views

Equation for the length of a chord parallel to either the minor or major axis in an ellipse

I am looking for a way to compute the length of any chord parallel to the minor (or major) axis of an ellipse. In all cases I know the lengths of both axes, and the distance between the chord and axis ...
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0answers
140 views

What's a bi-rhombus? [on hold]

Please, our class is desperate. We need to know what is a bi-rhombus. Our teacher asked us to do a graded project involving this
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0answers
125 views

Meaning of a bi-rhombus [on hold]

I need to figure out what a bi-rhombus is to do this question. My teacher gave me this question in class. (a) Explain the relationship between an equilateral triangle, a rhombus and a bi-rhombus. ...
3
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1answer
24 views

How prove that $|AB - CD| + |AD - BC| \geq 2|AC - BD|$ in cyclic quadrilateral?

Let ABCD be a cyclic quadrilateral. How show that $|AB - CD| + |AD - BC| \geq 2|AC - BD|$?
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0answers
53 views

Is there a golden pyramid?

Related to golden ratio: Golden rectangle is said to be the most aestheticaly pleasing among rectangles: This question mentions golden triangles: On the other hand, another question mentions ...
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3answers
45 views

Euclidean space and Euclidean geometry

If we have a Euclidean space $\mathbb{E}^2$, how can we define the Euclidean geometry,i.e. how to determine point,line,or some other things on it?
4
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2answers
95 views

What do you call geometric patterns like this?

What do you call geometric patterns like this ?