I apologize if this is old. Thing I found.

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I am uneducated in the maths and I have self taught myself algebra and introductory calculus. I sit up at night and think of things having to do with maths because I enjoy it and it is great fun for me.

I am sure that many of the things that I think of have already been found by people throughout history, but I will post the things that I figure out in this thread if it is all right with the moderators. I doubt that these have any applications but it is fun.


Take two random numbers and calculate their squares.
Find the difference between the two unsquared numbers.
Multiply each unsquared number by the difference between the two numbers.
The sum of the two products calculated above is equal to the difference between the two squared numbers found in the first step.

This is not proof but is example:
5, 19
19 - 5 = 14
(5 * 14 = 70) , (19 * 14 = 266)
(70 + 266 = 336)

(5^2 = 25) , (19^2 = 361)
(361 - 25 = 336)


Thank you for reading this. I apologize that it is messy. I wish I could state this algebraically, but I do not know how to. I apologize if this is wrong place.


I apologize, someone sent me a message to tell me that this is simply the difference between two squares for which these is a formula. I apologize for wasting time for you all.
 
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Answers and Replies

  • #2
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a, b real numbers
with binomial
a(a-b)+b(a-b)=(a-b)(a+b)=a2-b2
or with computation
a(a-b)+b(a-b)=a2-ab+ab-b2=a2-b2

it's a basic binomial formula: (a+b)(a-b)=a2-b2
 
  • #3
HallsofIvy
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I am uneducated in the maths and I have self taught myself algebra and introductory calculus. I sit up at night and think of things having to do with maths because I enjoy it and it is great fun for me.

I am sure that many of the things that I think of have already been found by people throughout history, but I will post the things that I figure out in this thread if it is all right with the moderators. I doubt that these have any applications but it is fun.


Take two random numbers and calculate their squares.
Find the difference between the two unsquared numbers.
Multiply each unsquared number by the difference between the two numbers.
The sum of the two products calculated above is equal to the difference between the two squared numbers found in the first step.

This is not proof but is example:
5, 19
19 - 5 = 14
(5 * 14 = 70) , (19 * 14 = 266)
(70 + 266 = 336)

(5^2 = 25) , (19^2 = 361)
(361 - 25 = 336)


Thank you for reading this. I apologize that it is messy. I wish I could state this algebraically, but I do not know how to. I apologize if this is wrong place.


I apologize, someone sent me a message to tell me that this is simply the difference between two squares for which these is a formula. I apologize for wasting time for you all.
NO mathematical thought is a waste of time!
 
  • #4
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NO mathematical thought is a waste of time!
I couldn't agree more.

In fact, I love to find those curious identities. A few weeks agoI was sitting and performing some math in my calculator, when I found out that 1008 was multiple of 12. I already knew that 108 was a multiple of 12, but I'd never thought about numbers like 10000008, 100000000000008, and so on. It turns out that every number in the form 10000(abitrary number of zeros)8 is divisible by 12. Than I found a way of proving that - it was really cool.

I think everyone that loves math has found one of those interesting properties.

Don't be discouraged if someone told you it was "simply" an already known property.
 
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  • #5
Office_Shredder
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I couldn't agree more.

In fact, I love to find those curious identities. A few weeks agoI was sitting and performing some math in my calculator, when I found out that 1008 was multiple of 9. I already knew that 108 was a multiple of 9, but I'd never thought about numbers like 10000008, 100000000000008, and so on. It turns out that every number in the form 10000(abitrary number of zeros)8 is divisible by 9. Than I found a way of proving that - it was really cool.

I think everyone that loves math has found one of those interesting properties.

Don't be discouraged if someone told you it was "simply" an already known property.
By the way your result generalizes greatly (if you're interested google 'rule for divisibility by 9')
 
  • #6
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Oh, I thought the wrong number.
I found out those numbers are always divisible by 12, not 9!
I will correct my post.
 
  • #7
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Oh, I thought the wrong number.
I found out those numbers are always divisible by 12, not 9!
I will correct my post.
Yes. Also, your proof may not be a combination of two divisibility tests but you could have proven that these numbers are each divisible by 9*4 or 36 using the test for divisibility by 9 and the test for divisibility by 4.

I also enjoy using algebra and logic to prove certain numerical relationships. I found and proved a general relationship between recursives series of the form S(n) = 6*S(n-1)-S(n-2), triangular numbers and numbers of the form a(a + K) where K is a constant. Much of it was posted on this site but since there was not much interest, most of my work is just posted on my Yahoo list http://tech.groups.yahoo.com/group/Triangular_and_Fibonacci_Numbers/messages. But then I don't get any traffic there anyway.

Dont be discourage if people tell you that you discover an obvious result, keep at it and eventually you will be doing something novel like boolean math which had no useful purpose until the avent of computers!
 

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