Mathematics

WANNA LEARN MATH? SEE THIS:

MATHJAX

PATRICK

WYZANT

                                                                              

FOR THOSE WHO LOVES ZERO!

                                                                                 

                                                                                 

Some observations related to Ramanujan Number:

1. If negative cubes are allowed, 91 is the smallest possible number with similar quality 91 = 6^3 + (?5)^3 = 4^3 + 3^3
2. Interestingly 91 is also a factor of 1729. (91×19=1729)
3. If taking “positive cubes” would not have been a condition, Ramanujan number could have been ?91, ?189, ?1729, and further negative numbers
4. 1729 is also the third Carmichael number and the first absolute Euler pseudoprime.  (If you want to know more about this numbers I can discuss it in some other post)
5. Masahiko Fujiwara showed that 1729 is one of four positive integers (with the others being 81, 1458, and the trivial case 1) which, when its digits are added together, produces a sum which, when multiplied by its reversal, yields the original number:     1 + 7 + 2 + 9 = 19;                       19 x 91 = 1729
6. Till date only 10 Taxicab numbers are known.  Subsequent Taxicab numbers are found using computers.

                                                                                 

                         MATHS TRICKS:

1. Quick Square

If you need to square a 2-digit number ending in 5, multiply the first digit by itself plus 1, and put 25 on the end. That’s all!

252 = (2x(2+1)) & 25

2 x 3 = 6

625

                                                                                 

2. Multiplying by 9

To multiply any number between 1 and 9 by 9, hold both hands in front of your face, with fingers extended. Now drop the finger that corresponds to the number you are multiplying (for example, for 9 x 3, drop your third finger). Now count the fingers before the dropped finger (in the case of 9 x 3 it is 2) -- that‘s your first digit. Then, count the fingers after (again in this case, it’s 7). The answer is 27.

                                                                                 

To divide a large number by five, all you need to do is multiply by 2 and move the decimal point one space to the left:

195 / 5

Step 1: 195 x 2 = 390
Step 2: Move the decimal left; 39.0, or just 39

2978 / 5

Step 1: 2978 x 2 = 5956
Step 2: 595.6

                                                                                 

4. Subtracting from 1,000

To subtract a large number from 1,000, subtract all but the last number from 9, then subtract the last number from 10:

1000 – 648 = ?

Step 1: subtract 6 from 9 = 3
Step 2: subtract 4 from 9 = 5
Step 3: subtract 8 from 10 = 2

Answer: 352

                                                                                 

5. Calculate a Tip

If you need to leave a 15% tip, here is the easy way to do it. Work out 10% (divide the number by 10), then add that number to half its value and you have your answer:

15% of $25 = (10% of 25) + ((10% of 25) / 2)

$2.50 + $1.25 = $3.75