I have 5 pieces each is a triangle and they are supposed to somehow form a large triangle. Everyone has tried and we can't figure it out. I see lots of solutions online for 7 piece tangrams but nothing for a 5 piece.

Thank you
Zach

I suspect there are 180 solutions to this, and you are studying topology.

http://mathworld.wolfram.com/TriangleDissection.html

To solve the problem of forming a large triangle using 5 smaller triangles, you can try the following steps:

1. Start by identifying the shapes and sizes of the 5 triangles you have. Make sure that all the triangles are of the same size and shape.

2. Experiment with different arrangements of the triangles to form a larger triangle. It's important to note that the sum of the interior angles of a triangle is always 180 degrees. So, to form a large triangle, the angles of the smaller triangles should add up to 180 degrees.

3. One possible approach is to arrange three of the triangles at the vertices of an equilateral triangle. This would give each of the three vertices an angle of 60 degrees.

4. For the remaining two triangles, you can position them in a way that their angles complete the missing 60 degrees to form a straight line with the existing angles.

5. Continue experimenting with different arrangements until you find a configuration that allows all the triangles to form a large triangle. You can also try rotating or reflecting the triangles to explore additional possibilities.

Regarding your mention of topology and the number of possible solutions, it seems that you might be referring to more advanced concepts related to dissections of triangles. The website you referenced, MathWorld by Wolfram, provides information about dissections of triangles into smaller triangles, including various cases and solutions. If you are interested in exploring the topic further, the provided link can be a great resource.

Please note that the specific solution of forming a large triangle with 5 triangles may or may not be discussed in the online resources you mentioned. However, by following the steps outlined above and considering the properties of triangles, you should be able to find a solution to your problem.