# 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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### Intersection of a quadric and cubic in $\mathbb{P}^3$

My question is drawn from Miles Reid's textbook Undergraduate Algebraic Geometry, p. 116. Let $S \subset \mathbb{P}^3$ be a smooth, irreducible cubic. Let $l_1, l_2, l_3, l_4 \subset S$ be ...
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### Can ${n \choose 2}$ points be covered by lines determined by $n$ points?

Let $S=\{(a_1,b_1),\ldots,(a_{n \choose 2},b_{n \choose 2})\}$ be ${n \choose 2}$ points on the plane. Does there exist $n$ points, such that the lines determined by the $n$ points cover all the ...
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### minimize the area of convex hull of sum of 3 balls

How should we place 3 balls $B_1,B_2,B_3$ on the plane, if we want to minimize the area of convex hull of $B_1\cup B_2\cup B_3$ ? Balls can have boundary common points only -- the intersection of any ...
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### Is there a way to determine the cheapest way to cut a line if each cut costs the current length of a line?

I was reading through an example question for the UNSW Computing ProgComp and found a question they claimed to be impossible to solve without going through all possible solutions. From https://cgi....
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### Archimedes Classic Proof for Area of Circle: Love it but can't grasp one aspect…

The proof assumes that:... The perimeter of any CIRCUMSCRIBED regular polygon is GREATER than the circumference of the circle. ie: !http://www.themathpage.com/atrig/Trig_IMG/eval1.gif Is this an ...
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### Can a portion of a hypocycloid be a regular polygon?

Hypocycloids are curves that generally don't include straight lines. A significant exception is a hypocycloid with 2 cusps, generated by rolling one circle inside another having twice the radius of ...
Consider a set of $n$ points $x_i , i= 1 ... n$ belonging to some space $\mathbb{R}^m$. Given a point $p$ in the convex hull of the $x_i$ it is well known that we can represent $p$ as \$ p = \sum _i ^ ...