Question

Ellø guys ☺☺ .
Plz help me in this :

Can you give me some amazing Maths Fact for assignment??

If you can, then plz!

No spam ♻♻​

Answer 1

Answer:

1 . Ramanujan's Formula for π .

$\begin{lgathered}\sf \frac{1}{\pi} = { \Sigma}^{ \infty }_{n = 0} \frac{ \sqrt{8} (4n)! (1103 + 26390n)}{9801(n!) ^{4} {(396)}^{4n} } . \\\end{lgathered}$

The formula converges at an amazing speed and was in fact use in 1985 to compute 17,526,100 digits of π which was the world at the time.

2 .

$\begin{lgathered}\sf \frac{1}{4} + \frac{1}{ {4}^{2} } + \frac{1}{ {4}^{3} } + ..... = \frac{1}{3} . \\ \\\end{lgathered}$

One of the first infinite series to be sumed in the history of mathematics by Archimedes circa 250-200 BC.

3. A square with side length 9000 can be split five Pythagorean triangles.

See attachment 3 .

4. 2520 .

2520 ÷ 1 = 2520 .

2520 ÷ 2 = 1260.

2520 ÷ 3 = 840.

2520 ÷ 4 = 630 .

2520 ÷ 5 = 504.

2520 ÷ 6 = 420.

2520 ÷ 7 = 360.

2520 ÷ 8 = 315.

2520 ÷ 9 = 280.

2520 ÷ 10 = 252 .

The smallest whole number divisible by all whole number from 1 to 10 .

5 . $\sf 2^5.9^2 = 2592 .$

6. 132 = 13 + 32 + 21 + 31 + 23 + 12 .

132 is the sum of all the 2-digits numbers made from its digit . It is smallest such digit.

7 . 73939133 .

73939133 is the largest known prime number if you keep removing digit from right, will always leave a prime number.

8 .2019 is the smallest number that can be written in 6 ways as the sum of the squares of 3 primes :

7² + 11² + 43² = 2019 .

7² + 17² + 41² = 2019 .

13² + 13² + 41² = 2019 .

11² + 23² + 37² = 2019 .

17² + 19² + 37² = 2019 .

23² + 23² + 31² = 2019 .

9 . 13² = 169 .

.................\/

................./\

.......31² = 961 .

10 . ..........111,111,111

........................×

.................111,111,111

_____________________________________

..........12,345,678,987,654,321 .

11. $\begin{lgathered}\sf \frac{3}{7} + \frac{2}{9} = \frac{5}{16}.\\ \\\end{lgathered}$

12 . Mirror fact

10² = 100 → 001 = 01² .

11² = 121 → 121 = 11².

12² = 144 → 441 = 21².

13² = 169 → 961 = 31².

13. Mathematical Oddities.

9² = 81 → 8 + 1 = 9.

45² = 2025 → 20 + 25 = 45.

55² = 3035 → 30 + 35 = 55.

99² = 9801 → 98 + 01 = 99.

297² = 88209 → 88 + 209 = 297.

703² = 494209 → 494 + 209 = 703.

999² = 998001 → 998 + 001 = 999.

14. Wonderful!

1³ + 5³ + 3³ = 153.

16³ + 50³ + 33³ = 165033.

166³ + 500³ + 333³ = 166500333.

1666³ + 5000³ + 3333³ = 166650003333.

........

15. An easy trick to find squares of numbers from 51 to 59.

51 × 51 = 2601.

52 × 52 = 2704.

53 × 53 = 2809.

54 × 54 = 2916.

55 × 55 = 3025.

56 × 56 = 3136.

57 × 57 = 3249.

58 × 58 = 3364.

59 × 59 = 3481.

Hence, it's done.

Answer 2

Answer:

Zero ( 0 ) is the only number which can not be represented by Roman numerals.

What comes after a million, billion and trillion? ...

Plus (+) and Minus (-) sign symbols were used as early as 1489 A.D.

2 and 5 are the only primes that end in 2 or 5.

An icosagon is a shape with 20 sides.