1. It is a tetrahedral number.
2. It is the sum of first 7 triangular number.
1 + 3 + 6 + 10 + 15 + 21 + 28 = 84
3. It is the sum of twin prime.
84 = 41 + 43
4. If you add 84 to 1000, the number 1084 you obtain is the smallest natural number which contains the five vowel in order.
1084 = One thousand eighty four
5. A hepteract is a seven dimensional hypercube with 84 penteract 5 faces. In geometry, a 7 cube or Hepteract is a seven dimensional hypercube with 128 vertices, 448 edges, 672 square faces, 560 cubic cells, 280 tesseract 4- faces, 84 penteract 5 faces, and 14 hexeract 6 faces.
6. It is an abundant number.
7. It is a 29-goanl number.
8. It can be partitioned 43 times with each term no longer than 2 and 631 times with each term no larger than 3.
9. It can be expressed as the sum of first 3 powers of 4 uniquely.
84 = 4^1 + 4^2 + 4^3
10. It is the maximal number of regions into which space can be divided by 7 spheres.
11. The probability of a pregnant woman having twins is 1 : 84.
12. According to Greek Anthalogy , Diophantus the Greek mathematician lived for 84 years. There is no other information known about his life except that comes from this problem which gives the result 84 on solving. The problem says---
This tomb holds Diophantus. Ah, how great a marvel! The tomb tells scientifically the measure of his life. God granted him to be a boy for 1/6 th of his life; and adding a twelfth part to this, he clothed his cheeks with down. He lit him the light of wedlock after a seventh part, and five years after his marriage he gave him a son. Alas, late born wretched child! After attaining the measure of half his father’s life, chill Fate took him. After consoling his grief by the study of numbers for four years, Diophantus ended his life. If Diophantus age is x years then we can write this algebraically as-- Which when solved gives x = 84. Diophanuts is better known as the father of algebra.
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