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25 votes
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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:
Bass's user avatar
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17 votes

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 ...
Oray's user avatar
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16 votes
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Slicing a rectangle

The area of ? is: Because: Working from there:
Paul Evans's user avatar
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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 ...
Rand al'Thor's user avatar
12 votes
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What percentage of blue?

Total number of triangles: w : white half parallelograms b : blue half parallelograms So... Image:
Traubenzucker's user avatar
11 votes
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Unlucky tiling: Arrange thirteen right isosceles triangles into a square

Solution:
nickgard's user avatar
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10 votes
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Professor Rackbrane: Count the triangles

We distinguish the triangles by how many of the short sides (ABCDEA) they use:
Parcly Taxel's user avatar
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9 votes

Can you help me out with this question?

The answer is - Explanation-
Shahriar Mahmud Sajid's user avatar
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 ...
Martin Ender's user avatar
  • 1,601
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):
u-ndefined's user avatar
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8 votes
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A circle touches two sides of a triangle and two of its medians

loopy walt's user avatar
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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 $1$:
JS1's user avatar
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7 votes

Slicing a rectangle

Here's an approach that I think is easier than the other approaches...
DaveBlackston's user avatar
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?
Jaap Scherphuis's user avatar
7 votes
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A geometric puzzle. What is the angle?

Here is a geometric proof: The angle p is therefore
loopy walt's user avatar
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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 (...
Rand al'Thor's user avatar
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):
Brandon_J's user avatar
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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
micsthepick's user avatar
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6 votes

Professor Rackbrane: Count the triangles

I have a general method for counting triangles in an given figure.
Florian F's user avatar
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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
Rand al'Thor's user avatar
5 votes
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How many cubes is this tringle made of?

My answer:
Weather Vane's user avatar
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5 votes
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Independent Triangles with Straight Lines

I created 11 independent triangles with ...
Sleafar's user avatar
  • 18.1k
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) ...
Penguino's user avatar
  • 14k
5 votes
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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:
Jaap Scherphuis's user avatar
4 votes
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Two difficult "Seventeen right isosceles triangles into a square" tilings

Here are the solutions to both questions:
phenomist's user avatar
  • 13.6k
4 votes
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Five graded difficulty isosceles right triangle into square tilings

Here are the solutions to the five problems.
phenomist's user avatar
  • 13.6k
4 votes
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Surrounding an equilateral triangle

A trivial solution?
Daniel Mathias's user avatar
3 votes

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

Does this count as 8 triangles?
昨晚忘記呼吸's user avatar
3 votes
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20 right isosceles triangles into a square

Here are at least two solutions (up to reflection and rotation)
phenomist's user avatar
  • 13.6k
3 votes

Independent Triangles with Straight Lines

with 7 lines could be same as the previous answer
DrD's user avatar
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