Math History ala a Digital Clock
A slight variation this week for something unusual....(i.e. a prime example of the strange things mathematics teachers do!
Carlton Lane, mathematics professor at Hillsborough Community College, suggests that during specific periods of every day, a digital clock reminds us of aspects of the history of mathematics. His examples:
 2:34 Counting: 2,3,4, ...
 2:35 Addition: 2+3=5
 2:36 Multiplication: 2x3=6
 2:37 Primes: 2,3,7
 2:38 Cubes: 2^{3} = 8
 2:39 Squares: 9=3^{2}
 2:40 Even Numbers: 2,4,24,40,240
 2:41 ThreeDigit Primes: 241
 2:42 Subtraction: 42=2
 2:43 Permutations: of 2:34 where it all started
 2:44 Base 10: 2+4+4=10; 24+4=28; 2+8=10; 2+44=46; 4+6=10
 2:45 Division and Decimals: 2/4=.5
 2:46 Arithmetic Progression: 2,4,6
 2:47 Abundance of Primes: 241, 247
 2:48 Geometric Progression: 2,4,8
 2:49 Palindromes: 2+4+9=15; 24+9=33; 2+49=51, whence 153351
 2:50 Long Division and Decimals: 50/2= 25.0
 2:51 Infinitude of Primes: By induction
 2:S2 Symmetry: Turn clock upside down
 2:53 Commutivity: 2+3=5=3+2
 2:54 Definition: 254 centimeters = 100 inches
 2:55 Odd Numbers: (At last!)
 2:56 Perfect Squares and Computers: 256=16^{2}, 16 is base of hexidecimals
Obviously, someone named Lane has too much "time" on his hands. Nonetheless, can you extend his time chart both before 2:34 and after 2:56 (as shown on the given clock)?
Solution:
Source: A. Lane's "Clock Arithmetic," College Mathematics Journal, Sept. 2001, p. 317
