Concept of the Exponential Law Prior to 1900

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Presentation transcript:

Concept of the Exponential Law Prior to 1900 The Radioactive Decay Law before Radioactivity The sound of a Tornado before the Freight Train 1978 Paper - Selected in 1991 among “Memorable Papers from the American Journal of Physics, 1933-1990”

L.J. Curtis, Amer. J. Phys. 46, 896-906 (1978). Memorable Papers 1933-1990, Amer. J. Phys. 59, 201-7 (1991)

ANCIENT FORMULATIONS Archimedes 300 BC “The Sand Reckoner”Characterized all sizes by a geometric progression in powers of (108)n using the arithmetic progression n “Method of Exhaustion” Seems to have integrated dx/x by a cumbersome rhetorical procedure. “Quadrature of the Parabola” Summed an infinite quartering series in Proposition 23.

Doubling Solution to Problem 79 As I was going to St. Ives, I met a man with seven wives. Each wife had seven sacks, each sack had seven cats, each cat had seven kits. Kits, cats, sacks, and wives, How many were going to St. Ives? Only me. The others were traveling from St. Ives.

An increased lifespan is NOT the problem!

TIME REVERSED HALFLIFE GRAIN FUTURES

Year 0 (1.2)0 = 1 Year 1 (1.2)1 = 1.2 Year 2 (1.2)2 = 1.44 Year 3 (1.2)3 = 1.728 Year 4 (1.2)4 = 2.0736 (2.0736-2.0)/(2.0736-1.728) x 12 = 2 + 5/9 = 2 + 33/60 + 20/602

Fibonacci Rabbit Pens APPROACHES THE LIMIT Ratio -> [sqrt(5)+1]/2 = 2/[sqrt(5)-1] = “Golden Section”

1661

mg - bv = ma a = g - (b/m)S a D t = g e -bt/m