About the Number 216 (two hundred sixteen)

SCC math professor Chris Benton gave a talk on the history of logarithms. This talk started with a brief overview of the history of multiplication. He used the multiplication problem 12 * 18 during his presentation and he mentioned that 216 is an interesting number.

   216 is an even, positive, integer
   216 is not prime
   216 has the prime factors:  2, 2, 2, 3, 3, 3 
   216 is the product of two numbers-cubed (2^3 * 3^3)
   216 is the sum of three numbers-cubed (3^3 + 4^3 + 5^3)
   216 is 6^3 (6 * 6 * 6)
   216 is Roman numeral CCXVI
   216 is the sum of the twin prime pair (107, 109)
   216 is a Harshad number (sum of its digits is a factor of 216)

The Wikipedia claims 216 is a untouchable number, but MathBabbler has not yet learned about untouchable numbers.

In addition, 216 is the magic constant for the following multiplicative magic square.

    +-------------+
    |  2   9   12 |         (row: 2*9*12 = 216)
    | 36   6    1 |         (row: 36*6*1 = 216)
    |  3   4   18 |         (row: 3*4*18 = 216)
    +-------------+         (diagonal: 2*6*18 = 216)
    (diagonal: 3*6*12 = 216)
    (column: 2*36*3 = 216)
    (column: 9*6*4 = 216)
    (column: 12*1*18 = 216)

To date, MathBabbler has not done anything with magic squares.

When MathBabbler last taught about creating and maintaining webpages, he emphasized that students should only use the 216 web-safe colors. [Note: The last time MathBabbler taught CSC185 was Spring 2002 (i.e. six years prior to the creation of this BAB).]

63 is not 666, but it is 6(6)(6).

Update::2013.08.08

pballew.blogspot.com::On This Day in Math - August 4

August 4th was the 216th day of the 2013.

216 is the smallest cube that's also the sum of three cubes.

	216 = 3^3 + 4^3 + 5^3 = 6^3

Source: Pat Ballew


Creator: Gerald Thurman [gthurman@gmail.com]
Created: 24 February 2008

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