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What is the most triangles you can make from a capital "H" and 3 straight lines?

Here's a solution for 7 triangles:
• 77.6k

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 ...
• 30.3k
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Slicing a rectangle

The area of ? is: Because: Working from there:
• 9,431
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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 ...
• 117k
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What percentage of blue?

Total number of triangles: w : white half parallelograms b : blue half parallelograms So... Image:
• 2,188
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Solution:
• 1,949
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Professor Rackbrane: Count the triangles

We distinguish the triangles by how many of the short sides (ABCDEA) they use:
• 7,720

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

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):
• 5,181
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• 21.3k
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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 $1$:
• 17.9k

Slicing a rectangle

Here's an approach that I think is easier than the other approaches...
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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?
• 53.4k
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A geometric puzzle. What is the angle?

Here is a geometric proof: The angle p is therefore
• 21.3k
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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 (...
• 117k

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):
• 9,327
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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
• 3,731

Professor Rackbrane: Count the triangles

I have a general method for counting triangles in an given figure.
• 30.6k
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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
• 117k
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• 14.5k
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Independent Triangles with Straight Lines

I created 11 independent triangles with ...
• 18.1k

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) ...
• 14k
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Triangles to diamonds

As Bubbler already noted in a comment, the final formula is To derive that, I will use the following facts and properties. Triangle areas In-radius Rhombus Now let's put all this together:
• 53.4k
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Two difficult "Seventeen right isosceles triangles into a square" tilings

Here are the solutions to both questions:
• 13.6k
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Five graded difficulty isosceles right triangle into square tilings

Here are the solutions to the five problems.
• 13.6k
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Surrounding an equilateral triangle

A trivial solution?
• 14.9k

What is the most triangles you can make from a capital "H" and 3 straight lines?

Does this count as 8 triangles?
• 767
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20 right isosceles triangles into a square

Here are at least two solutions (up to reflection and rotation)
• 13.6k