# Math Is Fun Forum

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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## #1 2007-07-17 17:37:49

bossk171
Member
Registered: 2007-07-16
Posts: 305

### x triangled

This was brought up by competearoundtheworld in a post but it wasn't related directly to his topic, it did however spark my interest, so here it is.

Competearoundtheworld  aroud the world said that you can triangle a number the same way you can square a number. I looked around and this is what I found:

When you triangle a number you are finding out how many circles it takes to build an equalateral trainge with the side of that value.

check this out: http://en.wikipedia.org/wiki/Triangular_number

Curious, I tried to Tetrahedronize numbers. I came up with:

It wasn't until I sat down to write this post did I come across the wiki:

http://en.wikipedia.org/wiki/Tetrahedral_number

none of this is stuff I've heard of before, but it seems pretty simple. I wonder if there is anything more anyone can add to my (and others) understanding?

There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

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## #2 2007-07-19 06:51:20

LQ
Real Member
Registered: 2006-12-04
Posts: 1,285

### Re: x triangled

Is that picture you have as an avatar really you?

And to your question, tetraheds can contain milk. Now that i've said that... Have a nice time.

I see clearly now, the universe have the black dots, Thus I am on my way of inventing this remedy...

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## #3 2007-10-24 17:53:21

landof+
Member
Registered: 2007-03-24
Posts: 131

### Re: x triangled

but isn't another possible formula for triangle numbers

???

or is it that I don't get what it really means?

Last edited by landof+ (2007-10-24 17:53:39)

I shall be on leave until I say so...

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## #4 2007-10-24 18:24:19

bossk171
Member
Registered: 2007-07-16
Posts: 305

### Re: x triangled

Distributive property

The more traditional way of writing it is the way you did, I just didn't realize that at the time.

There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

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## #5 2007-10-24 23:54:21

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: x triangled

Triangular numbers are made by adding the first n integers.
Then tetrahedral numbers are made by adding the first n triangles.

So does that mean that there's a special type of number that's made by adding the first n tetrahedrons?

Why did the vector cross the road?
It wanted to be normal.

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## #6 2007-10-25 00:00:58

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

### Re: x triangled

In general, such series of numbers (triangular, tetrahedral, pentatopic) are figurate numbers.

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## #7 2007-10-25 00:04:57

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,710

### Re: x triangled

And they are all on Pascal's Triangle

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #8 2007-10-25 02:55:58

bossk171
Member
Registered: 2007-07-16
Posts: 305

### Re: x triangled

Hmmm, I brought this up in July, and it was pretty much ignored. And now people seem interested.

I knew about triangle numbers being on Pascal's Triangle, but I didn't know tetrahedral numbers were.

And I'd never heard of pentatopic or figurate numbers. Interesting.

There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

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## #9 2007-10-30 05:18:04

mikau
Member
Registered: 2005-08-22
Posts: 1,504

### Re: x triangled

i define this to be stupid!

x squared is equal to the area of a square of side lengths x,

therefore, x triangled should be the area of an equalateral triangle with side lengths x!

which would be x^2sqrt(3)/4.

moreover, x circled would be 1/4pi(x^2).

This is more fun!

A logarithm is just a misspelled algorithm.

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## #10 2007-11-01 19:34:57

landof+
Member
Registered: 2007-03-24
Posts: 131

### Re: x triangled

exactly, but 'shaping' a number would be to make it a number that can be formed evenly into the 'shape' right?

I shall be on leave until I say so...

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## #11 2007-11-02 15:12:58

mikau
Member
Registered: 2005-08-22
Posts: 1,504

### Re: x triangled

I dunno. If we were to base it on the rule for x squared, we could say that 'shaping a number' (squaring it, triangling it) would mean getting the area of the regular polygon with side lengths given by that number. But by that rule, x circled makes no sense. Also, how does x cubed fit in?

hehe, i just felt like making sweeping objections. Wasn't really serious.

A logarithm is just a misspelled algorithm.

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## #12 2007-11-03 20:49:30

JohnnyReinB
Member
Registered: 2007-10-08
Posts: 453

### Re: x triangled

mikau wrote:

i define this to be stupid!

x squared is equal to the area of a square of side lengths x,

therefore, x triangled should be the area of an equalateral triangle with side lengths x!

which would be x^2sqrt(3)/4.

moreover, x circled would be 1/4pi(x^2).

This is more fun!

Actually , when you square a number, you are also calculating the number of circles needed to make a square with a side of that number...

So, x triangled works on the same principle

"There is not a difference between an in-law and an outlaw, except maybe that an outlaw is wanted"

Nisi Quam Primum, Nequequam

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## #13 2007-11-04 04:54:27

mikau
Member
Registered: 2005-08-22
Posts: 1,504

### Re: x triangled

i'm not sure i understand that explanation. What do you mean, number of circles? how big are the circles? and what do you mean by 'make a square'?

A logarithm is just a misspelled algorithm.

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## #14 2007-11-04 05:03:31

ganesh
Administrator
Registered: 2005-06-28
Posts: 35,503

### Re: x triangled

landof+ wrote:

exactly, but 'shaping' a number would be to make it a number that can be formed evenly into the 'shape' right?

Shaping a number????

Whats pentagoning a number??? And what would decagoning a number mean?

Even for quadrilaterals, only squaring is meaningful.
Rectangling a number or trapeziuming a number is absolutely meaningless to me. I say to me, because I don't know it has some meaning in the mathematics created till date!
In three dimensions, cubing is meaningful. What would sphering a number mean?????

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #15 2007-11-04 23:18:02

JohnnyReinB
Member
Registered: 2007-10-08
Posts: 453

### Re: x triangled

mikau wrote:

i'm not sure i understand that explanation. What do you mean, number of circles? how big are the circles? and what do you mean by 'make a square'?

I mean that ,for example, if you want to get 5 squared you:  ooooo
ooooo
ooooo
ooooo
ooooo

So, you find out how many units are needed to create a circle with that side.
Same with triangling it: o
oo
ooo
oooo
ooooo

I just meant circles as units. Sorry for creating confusion, Mikau. Peace?

"There is not a difference between an in-law and an outlaw, except maybe that an outlaw is wanted"

Nisi Quam Primum, Nequequam

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## #16 2007-11-05 03:14:54

mikau
Member
Registered: 2005-08-22
Posts: 1,504

### Re: x triangled

sure! But what says we can't put one big circle in a a square or triangle?

A logarithm is just a misspelled algorithm.

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## #17 2007-11-05 22:24:03

JohnnyReinB
Member
Registered: 2007-10-08
Posts: 453

### Re: x triangled

I am using circles to mean units, like building blocks. When you use units, they're generally the same size, no?

Once again, sorry for the confusion...

"There is not a difference between an in-law and an outlaw, except maybe that an outlaw is wanted"

Nisi Quam Primum, Nequequam

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## #18 2008-01-08 04:22:46

iheartmaths
Member
Registered: 2008-01-08
Posts: 31

### Re: x triangled

Funny enough, I was working on this the other day. Being the amateur that I am, I had no idea this already existed. I was fairly certain someone had done this already, but I wasn't sure of its name. Sure enough, I came up with the same: n(n + 1)/2

Don't quote me on that.

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## #19 2008-01-08 04:51:50

bossk171
Member
Registered: 2007-07-16
Posts: 305

### Re: x triangled

iheartmaths wrote:

Funny enough, I was working on this the other day. Being the amateur that I am, I had no idea this already existed. I was fairly certain someone had done this already, but I wasn't sure of its name. Sure enough, I came up with the same: n(n + 1)/2

What approach did you use to come up with that. I ask, because I too played around with that before I knew that some else already had (although I assumed someone did, I just thought it to be more fun on my own).

There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

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## #20 2008-01-08 05:19:22

iheartmaths
Member
Registered: 2008-01-08
Posts: 31

### Re: x triangled

bossk171 wrote:
iheartmaths wrote:

Funny enough, I was working on this the other day. Being the amateur that I am, I had no idea this already existed. I was fairly certain someone had done this already, but I wasn't sure of its name. Sure enough, I came up with the same: n(n + 1)/2

What approach did you use to come up with that. I ask, because I too played around with that before I knew that some else already had (although I assumed someone did, I just thought it to be more fun on my own).

I drew out the diagrams of the triangles and realized that the number of dots is equal to the sum of the bases of every preceeding triangle. Obviously, that wouldn't be practical for the larger triangles like base 2000. So, the second thing I noticed was that as the base increases by 1, it shares a relationship to the total number of dots that increases by 0.5
1 = 1
2 = 1.5
3 = 2
4 = 2.5
5 = 3
So, a triangle with a base of 1 will have 1 dot. But a triangle with a base of 2 with have 3 dots. I know I'm terrible at explaining this.
So, naturally from that I got that the answer should be something like n (number) * d (decimal, .5, 1, 1.5, etc.). The obvious problem is that when you get to numbers like 2000, it's harder to predict what the number to multiply by is. So, I needed another forumla. Which I soon found that (n + 1)/2 gave me that. Then I just combined the two into n((n+1)/2). and it would look something like this, which makes the relationship a little easier to see:
1 * 1 = 1
2 * 1.5 = 3
3 * 2 = 6
4 * 2.5 = 10
5 * 3 = 15
Sorry, I know I don't do the best job at explaining, but I try, I try.

Last edited by iheartmaths (2008-01-08 05:54:13)

Don't quote me on that.

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