Believe your teacher when he says, "Mathematics is Everywhere."
From marketing to shopping, from buying to selling, from eating to playing, from watching movies to making them, Mathematics is everywhere. The least place you would be expecting it, would be where you would find it the most.
There are innumerable amazing theorems, beautiful proofs, logical thoughts in mathematics that most of the people in common don't know and should be knowing.
So here we are counting upon our list of Top 10 Mind Blowing Facts About Mathematics that may be some proof, theorem or thought that can completely blow your mind.
These statements are surely going to make you think hard about what you were thinking about that particular topic, so buckle up as we're diving straight to the list.
#10. Number Theory
Have you ever wondered why one two three is written like 1 2 3 ???
The
numbers we write are made up of algorithms (1,2,3,4,etc) called Arabic
algorithm to distinguish between Roman algorithms (I ,II ,III ,etc) .
the
Arabs popularize these algorithms but their origin goes back to the
Phoenician merchants that used them to count and do their commercial count ability .
#9. 0.99999.... = 1
No, the above written is not an approximation. It is a solid proved truth in mathematics. There are many proofs for this statement, but the one that's easiest to understand and absolutely genius is this:#8. Deck Of Cards
You will never look at a deck of cards the same way after reading this.
How many ways can a deck of cards be arranged?
Any mathematician will tell you that it’s a simple calculation - the answer is 52!
But how big is this number really?
52 Factorial has found a creative way to visualize this number. I have simplified it for better readability.
Set a timer so that it would take52!
seconds for it to reach 0.Choose any spot on the equator. You have to walk around the Earth along the equator. But there’s a the catch — you can only take one step every billion years.
(Did I leave the stove on?)
After you complete one journey around the equator and reach the point where you started, remove one drop of water from the Pacific Ocean.
(No peeking at the timer!)
Now repeat the whole process — walk around the Earth at one billion years per step, removing one drop of water from the Pacific Ocean every time you circle the globe. Continue until the ocean is empty.
(How long has it been?!)
After you have emptied the Pacific Ocean, take one sheet of paper and place it flat on the ground.Fill the ocean back up and start the entire process all over again, adding a sheet of paper to the stack every time you empty the ocean.Do this until the stack of paper reaches the Sun.
(You’re almost there!)
Once the stack reaches the Sun take it down and do it all over again.One thousand times more.
(Is there a point to this?)
Surely the timer must have reached 0 by now?
Nope.
You’re only done with one-third of the time!
*52! = 806581751709438785716606368564037669752895054408832778240000000000000
I know you didn't even read the whole number.
#7. Surface Area Of Sphere
Well ever wondered how the Surface Area of a Sphere was derived?
Well here is a great visualization to alter your perception.
Step 1: Cut the sphere in the following way.
Step 2: Spread the cut out part across the paper.
Step 3: Collate the pieces together in the following way
Step 4: Spread the areas out separately to form a sine curve
Step 5: The area of the sine curve is the surface area of the sphere.
#6. Can You Prove 1+1=2?
If you have 1 apple and someone gives you 1 apple you have 2 apples right?
Yet the proof that 1 + 1 = 2 is many pages long.
Alfred
North Whitehead and Bertrand Russell wrote The Principia Mathematicia, a
three-volume work on the foundations of mathematics.
When they started in 1903 they thought they'd be finished in one year but it took them 10 years.
Only in the second volume, after 362 pages they come to the conclusion that 1 + 1 = 2.
Learning addition now really made things easier, didn't it?
#5. Most Beautiful Number
Ever heard of the world’s most beautiful number?It’s
This number is known as the Golden Ratio, Golden Proportion, Divine Number, Divine Section and Golden Mean. In Mathematics, two numbers are said to be in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two.
Using this concept, here is a golden rectangle:
A golden rectangle (in pink) with longer side a and shorter side b, when placed adjacent to a square with sides of length a, will produce a similar golden rectangle with longer side a + b and shorter side a. This illustrates the relationship
.
Additionally, the ratio of two successive Fibonacci numbers is very close to the golden ratio.
So
what’s so special about this number? The golden ratio has been used for
centuries in paintings, architecture, in preparing artificial designs,
as maintaining proportions conforming to the golden ratio has always
proved to be attractive and visually appealing. This ratio is found
everywhere in nature, from the arrangement of branches on trees and
veins in leaves to the human body.
Here are some examples:
Taj Mahal, India
CN Tower, Toronto
Notre Dame, Paris
Human Face
Google
Now who was not agreeing to Mathematics Being Everywhere...?
#4. The Black Hole Number
Did you know that the number 4 is designated as the black hole number?
Think of any word, name, thing etc.
For e.g. the word ‘‘mathematics”, has eleven letters.
Now ‘eleven’ in turn has six letters.
‘Six’ has three letters.
‘Three’ has five letters.
‘Five’ has four letters.
And how many letters does ‘four’ have?
FOUR!
Think of any other word and you’ll arrive at the same dead end.
Black hole number, people.
#3. Special Number
The number is 6174.Wait, are you thinking this a randomly generated number?
You will know soon enough.
Try this:
- Take any four-digit number, using at least two different digits. Repeated digits, such as 1111, will not work, because you will just end up with 0 after step 3.
- Arrange the digits in ascending and then in descending order, adding leading zeros if necessary. Add leading zeros if necessary – for example, 4560 in ascending order is 0456 and 6540.
- Subtract the smaller number from the bigger number.
- Go back to step 2 and repeat the process.
For example, choose 6532:
6532 – 2356 = 4176
7641 – 1467 = 6174
Another example, choose 4906:
9640 – 0469 = 9171
9711 – 1179 = 8532
8532 – 2358 = 6174
7641 – 1467 = 6174
6174 is known as Kaprekar’s constant, named after Indian mathematician D. R. Kaprekar.
#2. Logic Fails Before Mathematics Sometimes
What if I say,
1+2+3+4+5+6+7....=−1/12
Yes, sum of all positive integers up to infinity is negative, sounds crazy?
It's not.
I am going to prove the above equation. Bear with me.
Don't worry, I am not the one behind this magic, its Mr. Srinivasa Ramanujan.
#1. The Still Unsolved...
Let's try out the conjecture on the even number 4. 4 can be expressed as 2 + 2. 2 is a prime, so the conjecture holds up.
Same goes for a larger number like 28. You can express 28 as the sum of the prime numbers 5 and 23, or 11 and 17.
You can go even higher—why not try something crazy like 12,345,678? That can be expressed as the sum of prime number 20,297 and 12,325,381.
(You can try it yourself on this Goldbach calculator.)
There you have it, Top 10 Mind Blowing Facts About Mathematics that most people are unaware of.
I hope you liked this collection of amazing mathematics fundamentals, logic thoughts, proofs, theorems etc. and if you did don't forget to share this with your friends to blow their mind too!
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Until next time do give thought to these amazing facts about Mathematics that you never knew, and stay tuned for the next Top 10 Today list.
Peace Out!
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