25
votes
Accepted
What is the most triangles you can make from a capital "H" and 3 straight lines?
Here's a solution for 7 triangles:
- 71.4k
22
votes
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17
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Slicing a rectangle
First of all, by a simple geometry principle:
$\triangle CED$ and $\triangle AED$ have the same base $|ED|$ and the
area ratio between $\triangle CEF$ and $\triangle CFD$ has to be the
same as the ...
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16
votes
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14
votes
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Prove why this mechanical linkage for a triangle centroid works
The proof is in two parts, corresponding to the two linkages which are joined to each other at a single point. For each part, I'll try to both explain in words and illustrate on the picture you've ...
- 115k
12
votes
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What percentage of blue?
Total number of triangles:
w : white half parallelograms
b : blue half parallelograms
So...
Image:
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11
votes
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9
votes
Slicing a rectangle
Now that we have two correct answers, I figured I'd present my own approach. It's similar to Paul's but doesn't work with the ratios of the side lengths, but instead directly with the ratios of the ...
- 1,601
9
votes
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Can you make 10 triangles with just 10 sticks?
Using non-overlapping sticks I get 36.
I'll give measurements and positions to make this easy to picture. Imagine we're drawing this on graph paper. Make one horizontal stick of width eight units. ...
- 779
9
votes
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The Erasmus isosceles triangle
It's possible if Professor Erasmus can reflect triangles when creating isosceles triangles. If we imagine them as being cut out of paper, this would be by flipping over the paper.
This is an ...
- 24.1k
9
votes
Triangle in a circle
A generalization to arbitrary centrally symmetric regions
A planar region is called centrally symmetric with respect to the origin, if for every point $P$ in the region also its reflection with ...
- 45k
9
votes
8
votes
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The Erasmus tedrahedron
No, it's not possible.
For any vertex, the three edges coming out of it must have distinct length, since otherwise the triangle must be isosceles as well as right, which forces an equilateral ...
- 24.1k
8
votes
Triangle in a circle
Imagine putting the three points within the circle one-by-one. We are only interested in the angular coordinates of these points. We use the first point to define the zero point for this angular ...
- 4,272
8
votes
3D? No-no! 3 Sides
Here is the solution to the puzzle (note the correction in "3,1,2,5" to "3,1,2,1,4", by comment here):
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8
votes
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7
votes
7
votes
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Special triangles in convex polygons
Here is a convex dodecagon made of $50$ of those triangles.
Can it be done with fewer?
- 47.3k
7
votes
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Find the least expense?
Assuming "transportation cost" means sum of distances to each of the three roads, and the side of the equilateral triangle has length $1$:
- 16.9k
7
votes
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7
votes
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Circle inscribed in triangle problem
Let's draw a few more points and line segments:
By looking at the side lengths,
Therefore, angle $BEC$ is
By quadrilateral $APEQ$, the angle $PEQ$ is $180-22=158$ degrees,
Commentary
Originally (...
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6
votes
What is the most triangles you can make from a capital "H" and 3 straight lines?
Here's one with six triangles (7 if you count triangles outside of triangles, which you don't):
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6
votes
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3D? No-no! 3 Sides
I was trying to post this 5 minutes before the other answer, but got snookered by camp wifi
- 3,669
5
votes
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Trianglify the Shapes
Here is one possible triangulation.
Note that all triangulations (that do not introduce extra vertices) will have the same number of triangles, which depends only on the number of sides in the ...
- 16.8k
5
votes
Accepted
5
votes
Can you make 10 triangles with just 10 sticks?
Two 5-point stars should do the trick! This solution uses 10 'sticks' (each stick spans vertex-to-vertex) of exactly the same length in 2D.
As someone commented briefly (sadly, it was deleted too ...
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5
votes
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That's a lot of triangles
Answer:
size 1: 48
size 4 : 30
size 9 : 20
size 16 : 12
size 25 : 6
size 36 : 2
Total: 118
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5
votes
Special triangles in convex polygons
It is possible to do better than a hexagon, if an irregular polygon is acceptable.
It is also possible to construct an equilateral triangle or a hexagon. On reflection (and thanks to @Hugh's comment) ...
- 13.3k
5
votes
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5
votes
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A triangle inside a triangle
The answer is
because, for example, if T2 has side-lengths
then a triangle T1 such as
More generally, we can consider T2 with side-lengths
and T1 with side-lengths
- 115k
Only top scored, non community-wiki answers of a minimum length are eligible