# Eikonal Blog

## 2010.01.14

### Mental calculation of cube root of a six-digit number

Filed under: mathematics, mentalCalculations, mind & brain — Tags: , — sandokan65 @ 13:34

Source: posting by Ray Langley to MentalCalculation@yahoogroups.com (Wed, Jan 13, 2010 at 8:27 PM); subject: “[Mental Calculation] Cube Root Extraction Trick”

 … Hand a calculator to a friend. Ask him to enter a two-digit number. Have him multiply his chosen number by his number, then multiply it again. Let’s say he chooses number 57.  57 X 57 X 57 = 185, 193  To extract the cube root of this number we must first memorize the cube roots for the single digits 1 thru 9: 1 = 1 2 = 8 3 = 27 4 = 64 5 = 125 6 = 216 7 = 343 8 = 512 9 = 729  Notice that : 2 cubed ends in 8 and 8 cubed ends in 2, 3 cubed ends in 7 and 7 cubed ends in 3, 4 cubed ends in 4, 5 cubed ends in 5, 6 cubed ends in 6, 9 cubed ends in 9. To derive the cube root of our number (185, 193), we divide it into two sections at the “comma”. The left section is 185 and the right section is 193. Now, we search for the first single digit cube that is NOT larger than 185. In this case, the number is 125, the cube of 5. So, 5 is the first part of our answer. Now we examine the right part of our number (193). Since this part ends in a 3, we refer to the single digit, which cubed, ends in 3. It is a 7. This becomes the right part of our solution. So, the answer is 57. This feat looks like it requires a great deal of mental ability, but it can be easily learned by anyone in a short time.

Related:

Similar here: More simple math wonders – https://eikonal.wordpress.com/2012/03/14/more-simple-math-wonders/ | Mental calculation of cube root of a six-digit number – https://eikonal.wordpress.com/2010/01/14/mental-calculation-of-cube-root-of-a-two-digit-number/ | Squares with just two different decimal digits – https://eikonal.wordpress.com/2010/01/05/squares-with-just-two-different-decimal-digits/ | Number theory finite concidental sums – https://eikonal.wordpress.com/2010/01/05/number-theory-finite-considental-sums/

## 2010.01.12

### Three requirements for evolution

Filed under: evolution, memetics — Tags: — sandokan65 @ 13:21
• 1) Variation between the individuals
• 2) Selection pressure based on differences in survival
• 3) Heritability of traits

## 2010.01.04

### Integrals with Gamma functions

Filed under: mathematics — Tags: , , — sandokan65 @ 20:00
• $\int_0^\infty \frac{\cosh(2yt)}{(\cosh(t))^{2x}} dt = 2^{2x-2} \frac{\Gamma(x+y)\Gamma(x-y)}{\Gamma(2x)}$, for $\Re x > |\Re y|$.
• $\int_{-i\infty}^{+i\infty} \frac{e^{its}ds}{\Gamma(\mu+s)\Gamma(\nu-s)} = \theta(\pi - |t|) \frac{2(\cos(\frac{t}2))^{\mu+\nu-2} e^{\frac{1}{2} i t (\nu-\mu)}}{\Gamma(\mu+\nu-1)}.$

Sources:

• “The Functions of Mathematical Physics” by Harry Hochstadt