How Many Triangles?

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23 Nov 2013 21:05 #126090 by ren
Replied by ren on topic How Many Triangles?
64
Convictions are more dangerous foes of truth than lies.

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23 Nov 2013 21:11 #126091 by
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ren wrote: 64


Finally, someone agrees!

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23 Nov 2013 21:29 - 23 Nov 2013 21:29 #126092 by
Replied by on topic How Many Triangles?

MCSH wrote:

Akkarin wrote:

MCSH wrote:

Alexandre Orion wrote:

MCSH wrote: 56... and can prove it:D


THAT'S OUR SAJJAD !!!!! :cheer:

... now, please show us.


Count those that have the bottom edge and the 2 other edges are equal (4)
Now we'll count those on left side and then multiply it by 2, (to cover those on right as well)
To count those on left, you can count those that their right edge is lowest line that comes from right, and then multiply it by 4.
They are:
3 small ones + 2 made of two small triangle + 1 made of 3 triangles + 3 that have bottom line (9)

Weird... it results in 76... I should've made a mistake in calculation last time :P


My solution:
Warning: Spoiler!


You are counting those at center twice ;) so it's 4 more :)


My mistake, well spotted!
Last edit: 23 Nov 2013 21:29 by .

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23 Nov 2013 21:36 #126093 by ren
Replied by ren on topic How Many Triangles?

Malcolm Serenity wrote:

ren wrote: 64


Finally, someone agrees!


What can I say? I don't like being wrong :P

did you think of them as dimensions or did you count ?
Convictions are more dangerous foes of truth than lies.

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23 Nov 2013 21:47 #126094 by
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[img

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23 Nov 2013 21:56 #126095 by
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way to ruin the fun Vesha

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23 Nov 2013 22:15 - 23 Nov 2013 22:16 #126096 by
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ren wrote:

Malcolm Serenity wrote:

ren wrote: 64


Finally, someone agrees!


What can I say? I don't like being wrong :P

did you think of them as dimensions or did you count ?


Neither. There's actually a mathematical way to do it, and that's how I did it. It all depends on how many unique lines come out of the bottom vertices
Last edit: 23 Nov 2013 22:16 by .

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23 Nov 2013 23:14 #126099 by ren
Replied by ren on topic How Many Triangles?
that's what i call dimensions. I looked at it in a sort of distorted 3d space. Like a non-cubic 4x4x4 cube of sorts :D
Convictions are more dangerous foes of truth than lies.

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23 Nov 2013 23:47 #126101 by
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ren wrote: that's what i call dimensions. I looked at it in a sort of distorted 3d space. Like a non-cubic 4x4x4 cube of sorts :D


Ahh. That makes sense!

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24 Nov 2013 00:03 #126104 by ren
Replied by ren on topic How Many Triangles?

Malcolm Serenity wrote:

ren wrote: that's what i call dimensions. I looked at it in a sort of distorted 3d space. Like a non-cubic 4x4x4 cube of sorts :D


Ahh. That makes sense!


really? When I do stuff like this it makes me feel like I'm about to discover the solution to ftl or time travel :D

how did you go about it?
Convictions are more dangerous foes of truth than lies.

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24 Nov 2013 00:43 #126107 by
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ren wrote:

Malcolm Serenity wrote:

ren wrote: that's what i call dimensions. I looked at it in a sort of distorted 3d space. Like a non-cubic 4x4x4 cube of sorts :D


Ahh. That makes sense!


really? When I do stuff like this it makes me feel like I'm about to discover the solution to ftl or time travel :D

how did you go about it?



Hahaha. I did it based off a a simple equation. For any "How many triangles" that are set up in this same way (intersecting lines originating from 2 vertices), you take the number of unique lines that originate from one of the bottom vertices and cube it. Thus, if you count the unique lines in the left or right vertices, you get 4. Cube it, and you get 64.

If you take just a plain triangle, there is only one unique line from each of the vertices. Thus, you get 1 triangle.

Attachment hd407c85.gif not found



If you add a new line to each vertex, you will find that you can form 8.

Attachment hcda3c0c.gif not found



Thus, 3 unique is 27.

Attachment hcb3e9f3.gif not found



And finally, 4 unique is 64
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24 Nov 2013 05:46 #126118 by Wescli Wardest
Replied by Wescli Wardest on topic How Many Triangles?
I know the math, but I was having a herd time visualizing all the variables. (probably spent too much time at work) :P

So I wrote down all the ones I could find. Or, I made a picture.


Warning: Spoiler!
Monastic Order of Knights
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24 Nov 2013 07:09 #126120 by
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Wescli Wardest wrote: I know the math, but I was having a herd time visualizing all the variables. (probably spent too much time at work) :P

So I wrote down all the ones I could find. Or, I made a picture.


Warning: Spoiler!


Another excellent way of solving :D

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24 Nov 2013 08:52 #126130 by Alethea Thompson
Replied by Alethea Thompson on topic How Many Triangles?
I have an answer for you, but you're not going to like it. Technically, if you went down into the very smallest particle break down of triangles the answer would continue on forever until it reached a point that it could go no further. Therefore, to simplify it the answer it translates into:

∞

:P Or better yet:

4. Challenge me, I'll prove it. LMAO!
Gather at the River,
Setanaoko Oceana

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25 Nov 2013 08:05 #126249 by Adder
Replied by Adder on topic How Many Triangles?
There is only 1 triangle, at any one time else the shape would not be a triangle. :dry:

Being silly of course... as the question is how many triangles occur in the prescribed pattern and I got to about 23 or 24 and then saw the other posts here with the answer. Oh thank you for saving me time
:silly:
Introverted extropian, mechatronic neurothealogizing, technogaian buddhist.
Likes integration, visualization, elucidation and transformation.
Jou ~ Deg ~ Vlo ~ Sem ~ Mod ~ Med ~ Dis
TM: Grand Master Mark Anjuu

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06 Dec 2013 06:42 #127407 by
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Answer 64.


Sites with the answer.
Website:
http://scienceblogs.com/startswithabang/2012/07/28/weekend-diversion-triangles-a-puzzle-and-beauty/

Here is a youtube video of the count. It shows all the counting from left and right side then eliminates double counts.
http://www.youtube.com/watch?v=MUrkkoKbzWE Answer 64.

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