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

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2answers
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Similar triangle proof in parallelogram

Can anyone help me with this task. From the top of a parallelogram $ABCD$ lowered the vertical $AM$ and $AN$ on the lines BC and CD . Prove that triangles $\triangle ABC$ and $\triangle AMN$ similar ...
4
votes
3answers
138 views
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Find the latus rectum of the Parabola

Let $y=3x-8$ be the equation of tangent at the point $(7,13)$ lying on a parabola, whose focus is at $(-1,-1)$. Evaluate the length of the latus rectum of the parabola. I got this question in ...
6
votes
1answer
60 views
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The lattice points in the real cone of some semigroups are just the integer cone of that semigroup.

I'm trying to solve an exercise in Fulton's book on toric varieties, and have reduced it to the following: Let $M$ be a lattice of rank $n$ with $M \otimes \mathbb{R} = V$, and $S$ be a finitely ...
6
votes
1answer
80 views
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Locus of a point on a fixed-length segment whose endpoints slide along orthogonal lines

Suppose we have some segment $AB$ of constant length that slides in such a way that its endpoints are moving along orthogonal lines. Let $P$ be a point in the segment so that $|AP| = a$ and $|PB| = ...
7
votes
3answers
1k views
+100

Splitting equilateral triangle into 5 equal parts

Is it possible to divide an equilateral triangle into 5 equal (i.e., obtainable from each other by a rigid motion) parts?
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0answers
18 views
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Geometric interpretation of adding dependence on a otherwise constant in a vector field.

So if i have $$ \vec{u} = \Omega r \vec{e_{\theta}}$$ Now if i take the curl $$\omega = 2\Omega\vec{e_z}$$ This is what we expect, we have a "rotating flow". Who's curl would be pointing in the z ...
2
votes
0answers
17 views
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Application of Jacobi's Theorem in Box Principle

Today I was going through Problem Solving Strategies by Arthur Engel, and found this in the chapter Box Principle Before the question it says it "treats a theorem of Jacobi and its applications" ...