Questions tagged [geometry]
For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, and angles.
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Is this Batman equation for real? [closed]
HardOCP has an image with an equation which apparently draws the Batman logo. Is this for real?
Batman Equation in text form:
\begin{align}
&\left(\left(\frac x7\right)^2\sqrt{\frac{||x|-3|}{|x|-...
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V.I. Arnold says Russian students can't solve this problem, but American students can -- why?
In a book of word problems by V.I Arnold, the following appears:
The hypotenuse of a right-angled triangle (in a standard American examination) is $10$ inches, the altitude dropped onto it is 6 ...
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What is the maximum volume that can be contained by a sheet of paper?
I was writing some exercises about the AM-GM inequality and I got carried away by the following (pretty nontrivial, I believe) question:
Q: By properly folding a common $210mm\times 297mm$ sheet of ...
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Does the square or the circle have the greater perimeter? A surprisingly hard problem for high schoolers
An exam for high school students had the following problem:
Let the point $E$ be the midpoint of the line segment $AD$ on the square $ABCD$. Then let a circle be determined by the points $E$, $B$ and ...
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How can a piece of A4 paper be folded in exactly three equal parts?
This is something that always annoys me when putting an A4 letter in a oblong envelope: one has to estimate where to put the creases when folding the letter. I normally start from the bottom and on ...
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Why can a Venn diagram for $4+$ sets not be constructed using circles?
This page gives a few examples of Venn diagrams for $4$ sets. Some examples:
Thinking about it for a little, it is impossible to partition the plane into the $16$ segments required for a complete $...
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Identification of a quadrilateral as a trapezoid, rectangle, or square
Yesterday I was tutoring a student, and the following question arose (number 76):
My student believed the answer to be J: square. I reasoned with her that the information given only allows us to ...
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How many sides does a circle have?
My son is in 2nd grade. His math teacher gave the class a quiz, and one question was this:
If a triangle has 3 sides, and a rectangle has 4 sides,
how many sides does a circle have?
My first ...
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What's the intuition behind Pythagoras' theorem?
Today we learned about Pythagoras' theorem. Sadly, I can't understand the logic behind it.
$A^{2} + B^{2} = C^{2}$
$C^{2} = (5 \text{ cm})^2 + (7 \text{ cm})^2$
$C^{2} = 25 \text{ cm}^2 + 49 \text{ ...
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Software for drawing geometry diagrams
What software do you use to accurately draw geometry diagrams?
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Why is the Penrose triangle "impossible"?
I remember seeing this shape as a kid in school and at that time it was pretty obvious to me that it was "impossible". Now I looked at it again and I can't see why it is impossible anymore.. ...
user736690
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How to distinguish between walking on a sphere and walking on a torus?
Imagine that you're a flatlander walking in your world. How could you be able to distinguish between your world being a sphere versus a torus? I can't see the difference from this point of view.
If ...
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What's new in higher dimensions?
This is a very speculative/soft question; please keep this in mind when reading it. Here "higher" means "greater than 3".
What I am wondering about is what new geometrical phenomena are there in ...
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Slice of pizza with no crust
The following question came up at a conference and a solution took a while to find.
Puzzle. Find a way of cutting a pizza into finitely many congruent pieces such that at least one piece of pizza has ...
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