• #### (expt 1.1 10) (expt 1.01 100) (expt 1.001 1000) --> 2.7169239...

From henhanna@gmail.com@21:1/5 to All on Tue Jun 28 18:48:14 2022
Place five pennies on a table top, all in mutual contact. (obviously, they must stack) ----------- a true, classic gem of a puzzle. i wish i knew this puzzle when i was young !

______________________

Can an ave. 14 y.o. understand (suss out) or figure out using pen and paper that ...

1. these numbers fall between 2 and 3 -------- or between 1 and 9 ?

2. these numbers are converging ... ?

(expt 1.1 10) ---> 2.593742460100002

(expt 1.01 100) ---> 2.704813829421529

(expt 1.001 1000) ---> 2.7169239322355203

(expt 1.0001 10000) ---> 2.718145926824356

(expt 1.00001 100000) ---> 2.7182682371975284

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• From Richard Tobin@21:1/5 to henh...@gmail.com on Wed Jun 29 09:04:19 2022
In article <3ba50b09-48b1-4a60-954c-caed5762b540n@googlegroups.com>, henh...@gmail.com <henhanna@gmail.com> wrote:

(expt 1.00001 100000) ---> 2.7182682371975284

This is unsurprising if you consider the binomial expansion of
(1-1/n)^n.

-- Richard

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• From Edward Murphy@21:1/5 to henh...@gmail.com on Wed Jun 29 20:39:47 2022
On 6/28/2022 6:48 PM, henh...@gmail.com wrote:

Place five pennies on a table top, all in mutual contact. (obviously, they must stack) ----------- a true, classic gem of a puzzle. i wish i knew this puzzle when i was young !

[spoiler space]

I think you can place #1 horizontally, then #2 #3 #4 horizontally on top
of #1 and forming a triangle with its center above #1's center, then #5 vertically so that it touches #1's center as well as the others. (This
depends on them being thin enough compared to their diameters.)

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