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**iamaditya****Member**- From: Planet Mars
- Registered: 2016-11-15
- Posts: 692

Can anyone please tell me something very interesting about maths. It could be an amazing or unbelievable thing, some good shortcut trick or anything which I will like very much. I will also tell you some if you tell me.:)

Practice makes a man perfect.

There is no substitute to hard work

All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,082

This might be interesting to you. I certainly find it interesting.

Start with the Fibonacci sequence:

1, 1, 2, 3, 5, 8, 13, 21, 34, .....

Divide each term by the one before:

1/1 = 1

2/1 = 2

3/2 = 1.5

5/3 = 1.6666

8/5 = 1.6

.......

The numbers converge on the golden ratio (phi) ; oscillating either side of that number.

If you compute 1/1, 1/2, 2/3, 3/5, 5/8, .......

the numbers converge to phi - 1, which is also 1/phi

Apparently, the sequence (of rationals converging on an irrational) has a special property (which I've forgotten for the moment) which means that a plant (such as a sunflower), growing a seed head from the centre, and with angular separation atan(phi), will be least likely to form cleavage planes which might cause the seed head to fall apart. So nature discovered the property first!

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Perhaps the most interesting thing that I ever saw was the Monty Hall problem. Not only does it have mind boggling probability, EM, the worlds highest IQ, tons of differing opinions, it has one more thing...goats! Yes, math ain't nothing without a couple of stinky goats thrown in.

http://www.mathisfunforum.com/viewtopic.php?id=20868

The most amazing things about it, were all personal. I became further convinced that EM was the only way to go if one desired to get the right answer an infuriating amount of times. Also, we were 2 of only 4 people in the world who knew that those Stanford and Duke university guys were not arguing with Marilyn. That would have been difficult enough, they were arguing with their own methods and colleagues who had hashed this problem to death in a statistics journal, many years before. RIPOSTP.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**iamaditya****Member**- From: Planet Mars
- Registered: 2016-11-15
- Posts: 692

The most interesting thing I have found in maths till now is the amazing relationship between Fibbonacci Series, The Golden Ratio and Nature. It has really amazed me. I also find pascal's triangle very interesting. There are 7 things that leaves me awestruck about pascal's triangle.

Practice makes a man perfect.

There is no substitute to hard work

All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,082

hi iamaditya

Then I think you'll find this interesting:

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**iamaditya****Member**- From: Planet Mars
- Registered: 2016-11-15
- Posts: 692

Yeah I know it.

This is one of the 7 things of the pascals triangle which i find very interesting.

*Last edited by iamaditya (2017-03-12 22:36:40)*

Practice makes a man perfect.

There is no substitute to hard work

All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 23,102

Hi;

325 is the smallest number to be the sum of two squares in 3 different ways:

and .425 also has a similarly property :

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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**iamaditya****Member**- From: Planet Mars
- Registered: 2016-11-15
- Posts: 692

Hmm, good!

There is no substitute to hard work

All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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**Monox D. I-Fly****Member**- Registered: 2015-12-02
- Posts: 809

iamaditya wrote:

Yeah I know it.

This is one of the 7 things of the pascals triangle which i find very interesting.

What are the other 6?

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**iamaditya****Member**- From: Planet Mars
- Registered: 2016-11-15
- Posts: 692

Actually there are 13. They all are listed below in brief.

1. A number of the nth row and nth position getting found out by Combiantion.

2.Existence of Fibonacci Sequence as bob showed above.

3.Shading Odd nos. in a Pascal's Triangle gives Sierpenski triangle series.

4.HCF of any row of a prime no. excluding 1 is that prime no. itself.

5.If you draw a hockey stick starting from an extreme end (that is a 1)and make a Hockey Stick,with only 1 number in the "J", the sum of all nos. in the stick = to the no. in the "J" of the hockey.

6.Adding nos. of the nth row give value as (2^n)

7.The nos. of the 2nd diagonal are the counting nos., the nos. in the 3rd diagonal are triangular nos., in the fourth are tetrahedral nos. and so on

8.The nos. of the nth row are the digits of 11^n.(From 11^5, it begans to overlap itself)

9.The pascal's triangle is symmetrical

10.Existence of catalan nos.

11.Pick any number inside Pascal’s triangle and look at the six numbers around it (that form alternating petals in the flowers drawn above). If you multiply the numbers in every second petal, you’ll end up with the same answer no matter which of the petals you start from.

12.Pick any counting number from along the first diagonal and square it. Then look at its two neighbours that lie deeper inside the triangle – they’ll always add up to that very same square number.

13.If you add up every single number in the first n rows, you’ll get the nth Mersenne number.

There is no substitute to hard work

All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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**cmowla****Member**- Registered: 2012-06-14
- Posts: 62

As I discovered, you can also modify Pascal's Triangle to help to construct the positive integer power sum formulas (image, video series) and the Bernoulli Numbers.

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**iamaditya****Member**- From: Planet Mars
- Registered: 2016-11-15
- Posts: 692

Hmm, excellent!

There is no substitute to hard work

All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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