Concept of the Exponential Law Prior to 1900

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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
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L.J. Curtis, Amer. J. Phys. 46, 896-906
(1978). Memorable Papers 1933-1990, Amer. J.
Phys. 59, 201-7 (1991)
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ANCIENT FORMULATIONS
Archimedes 300 BC The Sand
ReckonerCharacterized 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.
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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.
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An increased lifespan is NOT the problem!
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TIME REVERSED HALFLIFE
GRAIN FUTURES
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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
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Fibonacci Rabbit Pens
APPROACHES THE LIMIT Ratio -gt sqrt(5)1/2
2/sqrt(5)-1 Golden Section
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1661
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mg - bv ma a g - (b/m)S a D t
g e -bt/m