Mathematics Problem

Hi there!

Let me get right down to business.


I'm building a star-shaped building. It's got five 'legs' which connect in a hexagon shape. That's a five-sided polygon, right?


So I've got to fill in a floor in this space. It's larger than 10 meters across so I need to use quite a few pieces.

I don't have a diagram handy so let me try to describe it for you.



It's a five sided figure. Each of the sides is eight meters long. Each leg is turned 72 degrees, and that makes the hexagon have five 108 degree angles inside.

You'll probably need to make a diagram for this yourself.


Okay, now, I figure to fill it in I can split it into a triangle on one side, and a trapezoid on the other. Are you with me here? So then I further split the trapezoid into two triangles and a rectangle.


Now, what I need to know are these things:

From the short end of the trapezoid to the wide end, what is the distance? It's not 8 meters, 'cause the eight meter sides are bent on an angle. I forget how to figure this out myself.

Now, if I know that I can make the rectangle in the middle by making it eight meters on one side to match the short part of the trapezoid, and use the deduced length to make sure it'll match up with the triangle added later.

I then need to know how far across the wide end of the trapezoid is, so that I can make two triangle prims with the height and width to fit into the remaining triangle spaces.

Once I've got that, I should be able to work out the rest on my own.


If you math geniuses would be so kind as to show how you did it, I could really use a refresher on this. ^.^

Thanks!

This sounds like the perfect job for me, but I'm having trouble understanding what you need.
It sounds like you're building a 2-prim pentagonal shape with two boxes, using top-size, is that right? That's how I usually do it anyway.
And you want to know the distance from the base of the trapezoid to the top?
I don't get it. The distance should be the Z scale on the object properties... you can see and set it to what you want.
Post some pictures?

Here are some diagrams that might be helpful (the text isn't wildly relevant). The first figure under addendum #1 shows probably the easiest approach as all five triangles needed to make a pentagon are congruent, so you can get one prim right and then duplicate it and rotate them.

I used this method in the construction of a hexagonal roof once: when you get the first triangle cut right put a small alignment "pin" at the inside vertex of the triangle and link the two together with the pin selected last. This allows you to copy and rotate around the vertex instead of the center of the triangle. Once you've built your pentagon, you can unlink and delete the pins. I even used this to make a pitched (slanted) hexagonal roof, but I had to relearn trigonomety to do it.

As the next diagram in the link shows, the minimum number of triangles needed to construct a regular pentagon is 3, but they are two different shapes and good luck aligning them.

There is a theorem in geometry that says that any polygon can be reduced to a finite set of triangles, so if you need a really big one, look at the first diagram in the link to see how you can dice a regular pentagon into triangles and another pentagon. With enough patience you could make a sim sized pentagon. Hope that helps.

See the attachment - quick & dirty calculation of the dimensions needed, if I understood your way of cutting up the polygon correctly. (Oh and I forgot the height of the rectangle: 7.6m)

To verify the numbers for yourself: http://en.wikipedia.org/wiki/Sine (under "Right triangle definitions" has it explained in a very understandable fashion. The trig involved isn't that difficult and comes in very handy when building more than just a box prim

The method Malachi recommends is very usefull too, and not half as complicated as it sounds. It's well explained in the Ivory Tower Of Primitives. I've been relying a lot on that technique for my builds and would recommend you give it a try. It involved a lot less tinkering than cutting up polygons (which works ok with 5 sides might be hellish with 12 or more), if the starting prim is well dimensioned and the "pin" carefully positioned, the other prims will be correctly aligned from start, and should an error creep in, rebuilding the floor only takes a few copy & rotate operations

Thank you a lot! not only do I now know how to do what I was thinking of, you also gave me a better idea.

The way I created the five legs of the 'star' shape was by putting a prim at the axis of the first leg I made, then turning it. But a far superior way of doing this would be to make an equilateral triangle on the end of the leg and turn it on the axis of that, causing the whole thing to form a floor of five triangles. Thank you very muchly! ^.^