Interesting and amazing maths facts
The more one studies mathematics, the more mysterious it becomes, with powers that seem quite ‘spooky’ and almost magical at times.
Consider the Power of Pi: it seems such a simple concept, the ratio between the circumference of a circle and its diameter. As a fraction, that’s simply 22 over 7 but as an actual number, Pi is unknowable.
See the box for an approximate (!) statement of the value of Pi but in fact you could go on calculating it into eternity and never find a pattern or reach the end. So we just call it 3.142.
But consider how this “irrational” number seems to crop up everywhere. Pi is all over the natural world, wherever there’s a circle, of course, measuring patterns in the DNA double helix spiral or how ripples travel outward in water. It helps describe wave patterns or the meandering patterns of rivers.
π = 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823...
But Pi isn’t just connected with circles. For example, the probability that any two whole numbers among a random collection are "relatively prime" with no common factor is equal to 6 over Pi squared. Pi even enters into Heisenberg's Uncertainty Principle; the equation that defines how precisely we can know the state of the universe.
So Pi is just one example of the ‘magic’ of math. If you want more proof of this, consider the following:
Pi and pizzas are linked
You multiply Pi multiplied by the radius squared to find the area and multiply area by height to find the volume, That means the volume of a pizza that has a nominal radius of (z) and height (a) will, of course, be: Pi × z × z × aAnd strangely, if you enter Pi to two decimal places (3.14) in the your calculator and look at it in the mirror, you’ll see it spells ‘pie’.
Nature loves Fibonacci sequences
The spiral shapes of sunflowers and other patterns in nature follow a Fibonacci sequence, where adding the two preceding numbers in the sequence gives you the next (1, 1, 2, 3, 5, 8, etc.)
In a crowded room, two people probably share a birthday
It only takes 23 people to enter a room to give you an evens chance that two of them have the same birthday. With 75 people in the room the chances rise to 99 per cent!
Multiplying ones always gives you palindromic numbers
If you multiply 111,111,111 × 111,111,111 you get 12,345,678,987,654,321 - a palindrome number that reads the same forwards or backwards. And that works all the way back down to 11 x 11 (121) or just 1 x 1 (1).
The universe isn't big enough for Googolplex
A googolplex is 10 to the power of a googol, or 10 to the power of 10 to the power of 100. Our known universe doesn’t have enough space to actually write that out on paper. If you try to do that sum on a computer, you’ll never get the answer, because it won’t have enough memory.
Seven is the favorite number
You might have guessed that most people’s favorite number is 7 but that’s now been proven.
A recent online poll of 3,000 people by Alex Bellos found that around 10% of them chose seven, with three as the runner-up.
That might be because seven has so many favorable connections (seven wonders of the world, pillars of wisdom, seven seas, seven dwarves, seven days, seven colors in the rainbow). But it’s also true that seven is “arithmetically unique” - the only single number you can’t multiply or divide while keeping the answer within the 1-10 group.
Prime numbers help Cicadas survive
Cicadas incubate underground for long periods of time before coming out to mate. Sometimes they spend 13 years underground, sometimes 17. Why? Both those intervals are prime numbers and biologists now believe cicadas adopted those life-cycles to minimize their contact with predators with more round numbered life-cycles.
On the next page we look at how the answer is always 6174, how random patterns aren't really random and we reveal 14 other snap maths facts.
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Last update: 19 October 2015
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