What Are Some Mind Blowing Facts about Mathematics?

What are some mind-blowing facts about mathematics?

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. Most Beautiful Number Ever heard of the world’s most beautiful number? It’s φ=1.61803399. 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. 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. 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 a+ba=ab≡φ . 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 Human Face 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. 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. Six weeks lasts exactly 10! seconds In case you’re not a math guy, that doesn’t mean ten excited seconds, that’s ten factorial, which is 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10. There’s a really nice way to visualize this. There are. 3*4*5 seconds in a minute 6*10 minutes in an hour 8*√9 hours in a day 7 days in a week 2*√9 weeks in six weeks. (Explanation. √9 is 3, and √9 * √9 = 9, so you end up with 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10, which is 10!). Basel Problem The only item to appear both in the 10 equations list and in this list, it says that if you take the reciprocal of all the square numbers, and then add them all together, you get pi squared over six. If you’re a normal, sane human being, it was probably completely unexpected that the stuff on the left side has anything to do with pi, the ratio of a circle’s circumference to its diameter. THANK YOU !! Devesh Chaturvedi's answer to What are some lesser known but useful websites?