# Tag Info

Accepted

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

Here's a solution for 7 triangles:
• 78.6k
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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:
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### Professor Rackbrane: Count the triangles

We distinguish the triangles by how many of the short sides (ABCDEA) they use:
• 7,820

### 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):
• 5,191
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• 21.4k
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### A geometric puzzle. What is the angle?

Here is a geometric proof: The angle p is therefore
• 21.4k
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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 $1$:
• 18.1k
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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?
Accepted

### 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
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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
• 3,751

### 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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### Professor Rackbrane: Count the triangles

I have a general method for counting triangles in an given figure.
• 31k
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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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• 14.9k
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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:

### 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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### Independent Triangles with Straight Lines

I created 11 independent triangles with ...
• 18.1k
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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?
• 16.7k

### Prove why this mechanical linkage for a triangle centroid works

Explanation Proof sketch of Centroid Theorem (this is a good geometry puzzle)
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### What is the most triangles you can make from a capital "H" and 3 straight lines?

Does this count as 8 triangles?
• 767
Accepted

### 20 right isosceles triangles into a square

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

### Independent Triangles with Straight Lines

with 7 lines could be same as the previous answer
• 39.4k
Accepted

### How to map barycentric indices to a single integer?

[Note: OP has revised the question with a slightly different barycentric indexing scheme, which makes the following no longer quite right. I'll fix it up in a minute.] Number the rows of triangles ...
• 121k