Tagged Questions

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

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Can a section of a signed distance filed uniquely determine this field function?

A Signed distance field function is a field function which tells the minimum distance from any point in space to a specific object. Let $\phi(\vec{x})$ be a signed distance field function, an ...
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How to rotate a line based dimensions of a piece of paper

I have a line where I know the start and end point on a piece of paper with the dimensions of 8 1/2 inches x 11 inches. the start point is 5.6 inches from the right of the paper and 4 inches down ...
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a solid geometry problem

In the following 3D figure, we know that $AE \bot EC, AD \bot BD$, how to prove that $|ED| < |BC|$ ?
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What algebra is generated by $\mathrm{O}(2)$?

The unit complex numbers can be identified with the $2 \times 2$ special orthogonal matrices $\mathrm{SO}(2)$. The problem with $\mathrm{SO}(2)$, however, is that its not closed under $\mathbb{R}$-...
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Decomposition to rotation around arbitrary axis

In 3d, I have a $4\times4$ matrix $M$, which has only a rotation part and a translation part. In other words, I can compute $X'=RX+T$ ( with $R$ a $3\times3$ rotation matrix, $T$ a vector for the ...
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Find the length of the side of a right angle triangle inside a circle

Hello Stack Exchange. I have a question which has really been preventing me from making a certain program.In my program I need to find the length of AC using only AB and BD.The triangle is right-...
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How to solve the question related to geometry.

The question is : If $AB$ and $CD$ be two chords of a circle meets at $E$ then show that $\frac {AE} {CE} = \frac {DE} {BE}$. I don't find any clue to solve it.Please help me.Thank you in advance.
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What is this question asking for exactly?

So I'm given a question that asks: "A coffee filter is cone shaped with radius = 4 and height of 8. Suppose filter is filled with water up to a height of level h. Find an expression for the volume of ...
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Criterion for an affine isomorphism.

I am reading Don Taylor's book 'The Geometry of Classical Groups' and currently I am trying to understand the affine geometry section. There is a lemma which appears to be a criterion for a bijection ...
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Why can't I know if the figure is a rectangle, if angles c+d=180 and c=d?

I have a four sided figure, abcd (see the image, and ignore the EF part), where I know that angles c+d=180 and c=d. However, this isn't enough information to decide if this is a rectangle - why is ...
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Finding area of a part of a circle

I have the values of $L$, $R$ and $W$ in the picture below. The circle is drawn though the center of the rectangle. And the circle will always intersect the rectangle. How can I find the area of the ...
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How to find the area of the following isosceles triangle

I am stuck with the following problem : What is the area of an isosceles triangle whose equal sides are $20$ cm and the angle between them is $30^{\circ}$ ? It is a nineth standard problem and ...
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Fisheye equidistant projection mapping to fisheye stereographic projection?

I have a set of images captured by a wide-angle (fisheye) lens camera, and the projection is linear-scaled (equidistant). I would like to remap from this projection to fisheye stereographic, which is ...
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Geometric Description Of a Set In The Complex Plane

$$S_1=\left\{z:Im\left(\frac{z-z_1}{z-z_2}\right)=0, z_1,z_2 \in \Bbb C\right\}$$ $$S_2=\left\{z:Re\left(\frac{z-z_1}{z-z_2}\right)=0, z_1,z_2 \in \Bbb C\right\}$$ Can someone help me with the ...
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Division of a square and value of a disk

I cam across this problem and I really don't know how to solve it. So you start with a square that has value 1. You divide this square in 4 so that each new square has a new value, as given by the ...
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Find intersecting points on rectangle edges for line drawn inside it

Draw a rectangle ABCD. Draw a line inside it connecting any two edges GF. Draw a perpendicular bisector to line GF. At what points does the perpendicular bisector intersect the edges of the ...
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A generalization of the Sawayama lemma

Let $ABC$ be a triangle, let $D$ be a point on the line $BC$. The Thebault circle is a circle tangent $AD, BC$ and the circumcircle (yeallow circles in the following figure). I give a ...
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The function of distance between two points with time

Consider I have two points p and q, and a line segment l: y=mx+c (actually the enpoints of the segment are given). There is a circle with center q which is growing with time t, i.e. the radius r = k.t ...
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Shortest possible distance to locate an unknown road

You are stranded in the middle of a large desert and the only way home is a through a straight road, which unfortunately you do not know the location of. If the perpendicular distance from you to ...
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Prove that the Area of triangle whose vertices are $(0,0)$, $(b,a)$ and $(x,y)$ is $|by-ax|/2$

Prove that the Are of triangle whose vertices are $(0,0)$, $(b,a)$ and $(x,y)$ is $\displaystyle \frac{|by-ax|}{2}$. I found this problem in Number theory by George Andrews, but I wonder how it ...
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Intersection of Circles and Triangulation [closed]

Tracking a Cellphone CT1 to CT2 = 700m CT2 to CT3 = 1200m CT1 to CT3 = 1350m Cell Phone is 600m from CT1, 650m from CT2, and 800m from CT3 Draw a circle in each Cell Tower, indicating the distance ...
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Show that three circles are coaxal

Let $A_1, A_2, A_3, A_4$ are collinear, $B_1, B_2, B_3, B_4$ are collinear. Such that $A_1, A_2, B_2, B_1$ lie on circle $(O_1)$, and $A_3, A_4, B_4, B_3$ lie on circle $(O_2)$. Let $MNPQ$ be the ...
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Proof of the Isoperimetric Theorem in Higher Dimensions

I have read a couple of nice proofs for the isoperimetric theorem in 2 dimensions. Is there a simple proof for the isoperimetric theorem in $n$ dimensions? In other words, how do you prove that the $n$...
Six congruent isosceles triangles with equal sides $x$ cm are removed from the six corners of a paper in the shape of a regular hexagon of sides 20cm . The remaining portion is in the shoe of a 12 ...