Triangle investigations

nikki12 · 2011-04-30 21:58:21

I need some help to find an equation to work out how many triangles are in a 4-triangle, I know the answer is not 16 and I know there is an equation to work this out but I cannot figure it out.

Can someone please help and explain it to me please.

Thanks Heaps
Nicole:D

bobbym · 2011-04-30 22:27:10

Hi;

A 4x4x4 triangular grid?

nikki12 · 2011-04-30 22:28:20

Yes a 4x4x4 triangle.
thanks

bobbym · 2011-04-30 22:40:40

Hi;

Where n is the n x n x n

So for n = 4 you get 27.

You can count them to see if it is correct.

nikki12 · 2011-04-30 22:46:35

thanks,

that seems very complicated, will that formula work for all triangle grids no matter what the base number? Is there an equation that is standard for all triangles?

Thanks

bobbym · 2011-04-30 22:50:41

Actually that is a very simple and beautiful formula.

If you mean triangular grids of different n then the answer is yes.

For instance you can now see how many triangles are in this

16 x 16 x 16 triangular grid.

nikki12 · 2011-04-30 23:03:32

Im sorry to be painful but I cannot work it out if you have time can you please show me step by step so the formula and what im putting into it makes sense.

Thanks so much

bobbym · 2011-04-30 23:13:39

Hi;

This is the formula:

Substitute n = 16 in it.

1188

There is another formula that might be a little simpler:

John Conway in "The Book of Numbers," p 83 suggests,

when n is even:

when n is odd:

nikki12 · 2011-05-01 00:24:27

Thanks sooo much.
Is the John Conway formula always over 8 no matter what the number you are using?

bobbym · 2011-05-01 00:29:37

Hi nikki12;

Yes, just as long as you remember the first Conway formula is for n is even and the second one is for n is odd.

Can you now tell me how many triangles there are in a 3 x 3 x 3 grid?

By the way I forgot to greet you correctly, welcome to the forum!

nikki12 · 2011-05-01 00:47:06

3(3+2)(2*3+1)-1/8
3(5)(7)-1/8
3*35-1/8
105-1/8
104/8
=13

bobbym · 2011-05-01 00:53:05

Hi nikki12;

That is very good, that is the correct number.

nikki12 · 2011-05-01 00:57:09

yay! so in a 5 x 5 x 5 grid there would be 48
and in a 10 x 10 x 10 there would be 315 and so on.
You have been soo incredibly helpful thank you so much.

bobbym · 2011-05-01 01:00:46

That is correct. And you are welcome.

Math Is Fun Forum

#1 2011-04-30 21:58:21

Triangle investigations

#2 2011-04-30 22:27:10

Re: Triangle investigations

#3 2011-04-30 22:28:20

Re: Triangle investigations

#4 2011-04-30 22:40:40

Re: Triangle investigations

#5 2011-04-30 22:46:35

Re: Triangle investigations

#6 2011-04-30 22:50:41

Re: Triangle investigations

#7 2011-04-30 23:03:32

Re: Triangle investigations

#8 2011-04-30 23:13:39

Re: Triangle investigations

#9 2011-05-01 00:24:27

Re: Triangle investigations

#10 2011-05-01 00:29:37

Re: Triangle investigations

#11 2011-05-01 00:47:06

Re: Triangle investigations

#12 2011-05-01 00:53:05

Re: Triangle investigations

#13 2011-05-01 00:57:09

Re: Triangle investigations

#14 2011-05-01 01:00:46

Re: Triangle investigations

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