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## 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, ...
• 2:36 Multiplication: 2x3=6
• 2:37 Primes: 2,3,7
• 2:38 Cubes: 23 = 8
• 2:39 Squares: 9=32
• 2:40 Even Numbers: 2,4,24,40,240
• 2:41 Three-Digit Primes: 241
• 2:42 Subtraction: 4-2=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=162, 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