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Mathnerd will really like this one!
Take any four sequential numbers from the Fibonacci sequence.
Let's say, 1, 1, 2, 3 (the first four in the sequence).
Now, take the two outer numbers and multiply them together:
1 * 3 = 3.
Now, take the inner two numbers, multiply, and double:
(1 * 2) * 2 = 4.
And since the Pythagorean Theorem is A^2 + B ^2 = C^2, we do a little substitution...
(3)^2 + (4)^2 = C^2
so, that means that 25 = C^2
so C = 5
Which ends up giving the Pythagorean Triple: 3, 4, 5.
And, since the area of a right triangle is 0.5(base * height), the area of the triangle is: 0.5(3 * 4), or 6, which is what you get if you multiply the four numbers of the Fibonacci series that you used!
I discovered this in a book called "A Slice of Pi". It's pretty cool!
Here's another nifty one from the same book: You could probably use this one to win some bar bets...
A quick way to get the square of a number that ends in 5:
Let's say the number chosen to square is 45.
What you do is take the 4, add 1, then multiply.
so you would have 4 * (4 + 1) = 20.
Then, you add 25 onto the end. The answer being 2025.
A calculator will verify your result.
For three digit numbers (ending in 5) it's a similar procedure.
Let's say you have the number 895. Follow the same procedure.
89 * (89 + 1) = 8010.
Tack 25 onto the end, and you get 801025.
Utilizing a calculator again verifies the correct answer.
Pretty cool, huh??
Take any four sequential numbers from the Fibonacci sequence.
Let's say, 1, 1, 2, 3 (the first four in the sequence).
Now, take the two outer numbers and multiply them together:
1 * 3 = 3.
Now, take the inner two numbers, multiply, and double:
(1 * 2) * 2 = 4.
And since the Pythagorean Theorem is A^2 + B ^2 = C^2, we do a little substitution...
(3)^2 + (4)^2 = C^2
so, that means that 25 = C^2
so C = 5
Which ends up giving the Pythagorean Triple: 3, 4, 5.
And, since the area of a right triangle is 0.5(base * height), the area of the triangle is: 0.5(3 * 4), or 6, which is what you get if you multiply the four numbers of the Fibonacci series that you used!
I discovered this in a book called "A Slice of Pi". It's pretty cool!
Here's another nifty one from the same book: You could probably use this one to win some bar bets...
A quick way to get the square of a number that ends in 5:
Let's say the number chosen to square is 45.
What you do is take the 4, add 1, then multiply.
so you would have 4 * (4 + 1) = 20.
Then, you add 25 onto the end. The answer being 2025.
A calculator will verify your result.
For three digit numbers (ending in 5) it's a similar procedure.
Let's say you have the number 895. Follow the same procedure.
89 * (89 + 1) = 8010.
Tack 25 onto the end, and you get 801025.
Utilizing a calculator again verifies the correct answer.
Pretty cool, huh??
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