[Lex Computer & Tech Group/LCTG] Physics question

[Michael Alexander]

To extend Mitch Wolfe’s contribution:
Geometric progressions can indeed blow up.  In the limit of small increments, the geometric progression turns into the exponential, the function that can be proved to blow up faster than any other function.
    Mike Alexander




On Wednesday, September 27, 2023, 2:59 PM, Steve Parus via LCTG <lctg at lists.toku.us> wrote:

>From ‘The Magic of Numbers’ by Robert Tocquet, A. S. Barnes and Company: 
The problem of the Folded Paper page 109
The String Round the Equator page 112
Steve Parus

On Sep 27, 2023, at 2:30 PM, Mitchell I. Wolfe via LCTG <lctg at lists.toku.us> wrote:





The classic wheat and chessboard problem first recorded in 1256 also exhibits similar characteristics. Sometimes people start with a penny instead of a grain of wheat. Either way the nation's treasury is depleted well before the 64th square.

Even at much lower increments, Albert Einstein famously referred to compound interest as the eight wonder of the world.

Geometric progressions can blow up...

On 2023-09-27 13:40, Jon Dreyer via LCTG wrote:


2^10 is about 1000, so 2^50 would be about (2^10)^5 which is about 1000^5 or 10^15.

A ream of paper is 500 sheets and about 2" high so 1000 sheets would be 4" high so each sheet is 4*10^-3 high. Multiplying that by 10^15, which is the number of thicknesses of paper, we get 4*10^12". To convert to miles, divide by 12*5280, which is a bit more than 5*10^4, so we get somewhat less than 10^8 miles. An astronomical unit (Earth-Sun distance) is around 93,000,000 miles (I can still hear my dad's voice telling me that when I'm still a little kid) or about 10^8. So the stack of paper would approximately reach the Sun, way farther than the moon.

Checking my work, the height of the paper would be

(2**50)*(4*10.0**(-3))/(12*5280)
=> 71079539.57339798

which is indeed the same order of magnitude as an astronomical unit. Of course the mass of that folded stack of paper would be so huge that we'd have crashed into the Sun, or vice versa. So kids, don't try this at home!


--

Jon "Overshoot The Moon" Dreyer
Math Tutor/Computer Science Tutor
Jon Dreyer Music
On 9/27/23 1:04 PM, Steve Parus via LCTG wrote:
The change in diameter is equal to the change in circumference divided by pi.  Another one: if a piece of paper is repeatedly folded in half 50 times, would its thickness reach the moon? Steve Parus
 
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