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
votes
1answer
43 views

Is angle an instance of something more abstract than angle? [on hold]

Is an angle (as generally understood) best described as a relation or a quantity?
1
vote
1answer
16 views

Half secant in Circle

OT and OQP are tangent and secant respectively drawn from external point $O$ of a circle centered at $C$. Mid-point M of the secant is joined to center $C$,an arc is drawn with center $O$ to be ...
0
votes
0answers
9 views

Minimum Curvature for Circular Trapezoids?

I am thinking any shape that can be close to circular trapezoid having the surface curvature less than circular trapezoid. About the minimum curvature here. About the naming of circular trapezoids in ...
-5
votes
1answer
53 views

Whats the size of the X angle? [on hold]

Numbers on the image, are angles. measure X.
-2
votes
1answer
18 views

Relations involving the altitudes and orthocenter of a triangle [on hold]

For acute $\triangle ABC$ with altitudes $AD$, $BE$, $CF$, orthocenter $H$, and area $S$, I have to prove that: $$AB^2 + HC^2 = BC^2 + HA^2 = AC^2 + HB^2 \tag{a}$$ $$AB \cdot HC + BC \cdot HA + ...
-1
votes
1answer
24 views

$ DB\cdot DC = HA\cdot HB + KA\cdot KC.$ [on hold]

We have a point $D$ on the hypotenuse $BC$ of a right triangle $ABC$. $H$ and $K$ are the projections of $D$ on $AB$ and $AC$, respectively. I have to prove that: $$ DB\cdot DC = HA\cdot HB + ...
-1
votes
0answers
30 views

Geometry - points on a sphere [on hold]

Is there a way, or is it possible to describe a set of points on a sphere so that the they are distributed over the surface with maximal symmetry (or just evenly distributed)?
1
vote
1answer
29 views

Maximum number of equilateral triangles in a circle

I am stuck with a question. Given a circle with radius $x$ cm, what is the maximum number of equilateral triangles of side length 1 cm that can fit in the circle without overlapping or ...
0
votes
0answers
9 views

polar moment of area for nonplaner circle (cup)

Can somebody tell me the polar moment of area of chord for a sphere. for example when you cut a sphere at a point other than from center? Also polar moment of area for curved axis symmetry ?
8
votes
0answers
34 views

Congruent quadrilaterals in a tri-colored $72$-gon

I recently watched a movie (A Brilliant Young Mind) in which this problem appeared: Let the vertices of a regular $72$-gon be colored red, blue, and green in equal parts. Show that there are $4$ ...
1
vote
1answer
22 views

Selecting a basis such that the orientation is preserved

I need to map a polygon from a 3D plane to a 2-dimensional basis, do some processing, and project the result back to 3D. The vertices in the polygon is always ordered counterclockwise and this ...
-4
votes
0answers
15 views

What are the possible applications of homothety? [on hold]

What are the possible applications of homothety? Give me some examples, please. I know it can be used to proof coincidence of lines but what else?
0
votes
1answer
9 views

Isometries and Orthogonal Matrices

I know how to show that multiplying by an orthogonal matrix preserves the angle and distance between two vectors. I have seen everywhere that Orthogonal matrices are kind of related to rotations and ...
2
votes
4answers
22 views

Euclidean Geometry Quadrilateral Problem

When the quadrilateral is a square, rectangle, or parallelogram, the problem is very simple since X1Y1=X2Y2=X3Y3=a=b, but this falls apart when the quadrilateral is something like a trapezoid. How ...
0
votes
3answers
34 views

What is the relationship between the two radii and the two volumes? [on hold]

I don't understand this question, as it says to use the formulas for the volume and radius of a sphere. Formulas are $V=\frac43 \pi r^3$ $r=\sqrt[3]{3V/4\pi}$ Volume for the first sphere is ...
3
votes
1answer
29 views

How do I represent a Mobius Band Triangle Parametrically

I am trying to describe a Mobius band in the shape of a triangle like this: parametrically in terms of its $x$, $y$, and $z$ functions. Is this even possible? I know a basic mobius strip can be ...
0
votes
0answers
12 views

Is there any mathematical significance of the set-theoretic union of the hemispheric middle thirds of an oriented (e.g., rotating) sphere?

The title says it all, but we can add a synonymous formulation: Is there any mathematical significance of the region of an oriented (e.g., rotating) sphere whose latitudes are neither small nor large? ...
2
votes
0answers
13 views

Area of a sphere bounded by hyperplanes

Say we have a sphere in d-dimensional space, and k hyperplanes (d-1 dimensional) all passing through the origin. Is there a way to calculate (or approximate) the area of the surface of the sphere ...
0
votes
1answer
25 views

Dividing a Triangle by Connecting the Midpoints of its Sides

If $T$ is any triangle. Suppose we connect the midpoints of its sides forming four triangles. Does these four triangles have the same angles?
0
votes
1answer
19 views

Rotated parabola 2d vertex

I'm implementing an application where I need to get the vertex of a parabola, the parabola might be tilted; so it can have an angle with the x-axis not necessarily vertical or horizontal. Can I get ...
4
votes
3answers
53 views

Motivations for Hyperbolic Geometry

Why would one study hyperbolic geometry? I am only aware of the motivation where you give axioms for elementary euclidean geometry and then start to wonder wether the parallel axiom is necessary. You ...
0
votes
0answers
9 views

Solid Angle Formula Derivation

How to derive the formula for solid angle that is $2\pi(1-cos \theta)$ ? I searched on Wikipedia but could'nt understand the double integral method they provided.I searched Wikipedia:Solid Angle Can ...
0
votes
1answer
30 views

What rotation rules can be applied to stacked cubes to make a 3D spirograph?

If you could arrange building blocks for example toy cubes so that every next cube was tilted over its base by 20 degrees and rotated to it's right by 15 degrees, it would form a helical structure. ...
0
votes
0answers
20 views

Geometry rotation and common points

The equation of the rotation surface S which is created by the rotation of the hyperbola t: { $\frac{x^2}{9}-\frac{z^2}{4}=1$ ; $y=0$} is S:$\frac{x^2}{9}+\frac{y^2}{4} -\frac{z^2}{4}=1$,right? and ...
1
vote
0answers
21 views

Explanation of $\ker (\bar{m}-\bar{id})^2 \cap \{x_0=1\}$

Let $m$ be an isometry on $\mathbb{R}^2$ which is a composition of a reflection and a translation. The way to find the axis of the isomtry is by solving: $$\ker (\bar{m}-\bar{id})^2 \cap \{x_0=1\}$$ ...
-1
votes
0answers
43 views

Neccesary condition for perpendicularity [on hold]

Triangle $\mathit{BCD}$ lies in plane $P$ and $\mathit{AD}$ and $\mathit{DC}$ are perpendicular ($A$ is the top of the prism $\mathit{ABCD}$) $\mathit{AD}$ is perpendicular to $P$ if which of the ...
0
votes
0answers
8 views

Shear Stress of Circular non-planer plate

Shear Stress of plan circular plate is given by T = M/($2*t*$Pi*r^2) What will be Shear stress of non-Planer circular plate? For example chord of shpere or any other circular plate but curved in ...
0
votes
0answers
36 views

How to derive parametric equations of a curve from its geometric property?

A straight segment of line of variable length $h$ is attached to the origin $O$ and to the other free end $M$ another straight segment of variable length $a$ is attached . Its endpoint $P$ has two ...
0
votes
1answer
29 views

What is the radius of smallest circular disk large enough to cover every acute isosceles triangle of a given perimeter $L$?

What is the radius of smallest circular disk large enough to cover every acute isosceles triangle of a given perimeter $L$? Let $a,a,b$ are the sides of the isosceles triangle whose perimeter is ...
2
votes
2answers
54 views

How to determine a kind of distance between two permutations?

Let's define a distance between two permutation of length $N$: it is the minimum steps to change one to be another. "A step of change" means that exchanging any two elements' location. For example, ...
0
votes
1answer
38 views

Find the cosine of the angle at the vertex of an isosceles triangle having the greatest area

Find the cosine of the angle at the vertex of an isosceles triangle having the greatest area for the given constant length $l$ of the median drawn to its lateral side. I tried to solve this ...
0
votes
2answers
42 views

Two circle intersection: help on understanding a specific explanation

As someone with basic algebra knowledge, I am having trouble understanding Paul Bourke's explanation on "Intersection of two circles" on this page. The specific part that I don't understand is where ...
6
votes
1answer
56 views

Is this GRE math problem wrong?

I'm working out of the Manhattan GRE test prep book and I've come across a question that I can't figure out why they chose the answer they did. "Perpendicular lines m and n intersect at point (a,b), ...
0
votes
0answers
26 views

Find the maximum volume of the cylinder.

A cylinder is obtained by revolving a rectangle about the $x-$axis,the base of the rectangle lying on the $x-$axis and the entire rectangle lying in the region between the curve $y=\frac{x}{x^2+1}$ ...
1
vote
1answer
28 views

Equation to get the center point of the union of n ellipses?

If I have 3 ellipses that all intersect such as in image. How can I get the center point of the Union of all three ellipses? (Basically the center point of the red area in the image)
0
votes
0answers
4 views

Get LWH with volume ≥ X and smallest possible surface area

The formula for volume of a rectangular prism is $l\cdot w\cdot h$, and surface area is $2(wl + hl + wh)$. If I already have the volume (ie 20m²) as $X$, what are the optimal values for $l$, $w$, and ...
-3
votes
1answer
63 views

Find x in the triangle [on hold]

Find x, even if I turn out not
1
vote
1answer
21 views

Expression of reflection isometry in the complex plane

Using the fact that an anti-displacement in the plan has the form $$f(z) = a \overline{z} + b$$ I have done some computation to find the reflection about the line passing through two points $P$ and ...
1
vote
1answer
42 views

3D projection coordinates onto 2D plane to determine transformation matrix?

I'm not sure if there is an actual solution to this problem or not, but thought I would give it a shot here to see if anyone has any ideas. So here goes: I basically have three vertices of a rigid ...
1
vote
1answer
33 views

Surface area of circle extracted from a tube wall

I have made a hollow tube (thickness $1$mm) having inner radius $89$ mm and outer radius $90$ mm (length $400$ mm, can be higher). then I made a circular (circle radius $25$ mm) cut perpendicular to ...
0
votes
1answer
29 views

If $AD=999$ and $PQ=200$, find the sum of the radii of those incircles.

Let $ABCD$ be a convex quadrilateral with $\angle DAB =\angle BDC=90° $. Let the incircles of $\Delta ABD $ and $ \Delta BCD $ touch $BD$ at $P$ and $Q$, respectively with $P$ between $Q$ and $B$. If ...
-2
votes
1answer
29 views

Finding a point along a circle a certain distance away from another point [on hold]

How do I find the point(s) C (and C') which: lies on a circle centered at a point B with radius r is at distance d from point A A specific case would be: A = (0,0) B = (5,7) r=5 d=5
1
vote
3answers
37 views

Chords $AB$ and $AC$ divide the area of the circle into three equal parts.If the angle $BAC$ is the root of the equation,$f(x)=0$,then find $f(x)$

$A$ is a point on the circumference of a circle.Chords $AB$ and $AC$ divide the area of the circle into three equal parts.If the angle $BAC$ is the root of the equation,$f(x)=0$,then find $f(x).$ I ...
-2
votes
1answer
30 views

Geometry-Is this a correct question?

ABis parallel to CD.The values of the angles are a,3x,2x and z as shown in the figure.Also,2x+z=100 degrees.Now it is required to find the value of angle a.I tried hard but could not solve it.I ...
-3
votes
1answer
22 views

how to find the locus when distance from the origin is defined as d(x,y) = max { |x|,|y|},d(x,y) =a (where 'a ' is a non zero constant ) [on hold]

How to find the locus when distance of any point from the origin is defined as d(x,y) = max {|x| |y|} where d(x,y) = a ( where is a non zero constant) I have a very long list of questions like these ...
1
vote
1answer
14 views

When is a quadratic Bézier curve nearest the origin?

Consider a planet moving along a quadratic Bézier curve through points A B C, with $t$ = time: $\qquad \operatorname{curve}( t, A, B, C ) \equiv t' (t' A + t (2B - A)) \ + \ t (t' (2B - C) + t C ) $, ...
0
votes
0answers
16 views

Inverse curve fitting to a regular grid

Given a fixed grid of regular polygons (square, trianglular or hexagonal) and a curved path, (imagine a river), how do you generate or select the set of grid links that most closely matches the curved ...
3
votes
3answers
25 views

change of basis and inner product in non orthogonal basis

I have some vector, originally expressed in the standard coordinates system, and want to perform a change of basis and find coordinates in another basis, this basis being non-orthogonal. It's ...
1
vote
1answer
28 views

Maximum no. of laddoos of diameter $6$cm in a box of given dimension

What is the maximum number of laddoos having diameter of $6\text{ cm}$ that can be packed in a box whose inner dimensions are $24\times 18\times 17\text{ cm$^3$}$. I found that at the lower label ...
5
votes
2answers
63 views

Trapezoids in a square

Good day As part of a problem I need to show that AB is parallel to CD, with the given info on the image. All the segments marked red are equal, all 1-stripe grey equal etc. I'd like to prove ...