Questions tagged [geometry]
A puzzle related to shapes, geometric objects (polygons, circles, solids, etc.) of any number of dimensions, the relative position of figures, and the properties of space. Use with [mathematics]
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Which triangle has the larger area?
In the diagram, AFH, ABGF, ABCDE are all regular polygons.
Which triangle has larger area: red or blue? Or do they have the same area?
Note: Geogebra can be used to help, but an answer saying "...
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Triangles on regular pentagons
The two regular pentagons share a vertex and an edge. The side of the larger pentagon is twice that of the smaller one. Which triangle has larger area, red or blue? Or do they have the same area?
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The "e" in apple
I cut a thin slice from a spherical apple, cutting along a plane.
Then I realized, there is an "e" in apple.
Why is there an "e" in apple?
Hint:
OK, time to drop another hint:
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Sliding block puzzle: Get square to bottom centre
Consider these 10 blocks here, each with a different colour. One block has 4 squares, five have 2 squares and four have 1 square (the white area is unoccupied, and is not a block):
Text version:
<...
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Most symmetrical tangram
We discovered a new toy store near our house, and my daughter and I were very excited to check it out. We found a curious puzzle there and brought it home with us. After googling about it a bit, I ...
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Design a better magazine page layout. Or not.
I still read print magazines. Whenever I come across an interesting passage, I clip it out and post it on the refrigerator. I am surprised, however, how often a passage, even a relatively short ...
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Some almost smiley face facts ...
Very much inspired by excellent
An angle in a smiley face
While trying to solve it I noticed:
What if two (red) squares ABCD and A'B'CD' sharing C
do not have all 4 vertices AA'BB' on one single (...
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An angle in a smiley face
What's the angle in the following figure?
Clarifications:
The two squares share a vertex.
Each square has two vertices on the circle.
The squares are not of equal size.
Source: Inspired by a recent ...
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How to select P so that the angle APB is as large as possible?
Given a line and two points A and B, which point P on the line forms the largest angle APB?
Bonus question: How should we select P so that the angle APB is as small as it can be?
P.S.
I tried solving ...
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A crown in a polygonal cycloid
Take a regular polygon resting on one of its sides. Pick the left vertex of the side and start rolling the polygon to the right until that vertex touches the ground. Mark the location of that vertex ...
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If 3-D is too easy, go 4-D
It is a well-known puzzle that one can take a cube and make a single planar cut through it so that the intersection of the cutting plane and the cube is exactly a regular hexagon.
One can do an ...
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What is the probability that a random tetrahedron inside a sphere is intersected by the sphere's vertical axis? [closed]
A tetrahedron's vertices are independent uniformly random points in the interior of a sphere.
What is the probability that the tetrahedron is intersected by the sphere's vertical axis?
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A tour through a city of circular roads with no sharp turns
Anita lives in a city with a peculiar road system: every road is a circle (not necessarily of the same radius). The rules of the system are simple: no sharp turns. That is, if you are at a transversal ...
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