We next consider how much lifting would be required to build the a pyramid a number n layers high. Our unit of elevation is the height of one layer. We number the layers starting from the top and the kth layer has k2 blocks on it and each block there has to be raised n-k levels. The sum total of the changes in elevation is can be designated Σh. Σ(p,n) below is an abbreviation for the partial sum of n level of the series with power p. Using the formulas for the power series from the last post we can simplify the formula for the total amount of hoisting that is required.
In the check sum is 16*0+9*1+4*2+1*3=9+8+3=20. The formula gives 16*15/12=4*5=20.
Supplemental (Jan 14): Stumbled across a humorous satire involving Pythagoras by Lucian while googling him for the last post.
No comments:
Post a Comment