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An Infinitely Large Napkin

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Re: An Infinitely Large Napkin

#31

Post by fjsolwmv »

improv32 wrote: post #25
berbec wrote: post #23

Earlier quoted context omitted.

True if the napkin is perfectly flat. Any imperfections would negate the cancelation of opposing force, no? The drop off would only apply if the napkin has finite mass or infinite size, correct?

Here's a cool link I just found going over this exact scenario: https://www.mathpages.com/home/kmath530/kmath530.htm Interesting to note, the napkin creates a uniform gravitational field above and below it. Meaning that the force applied to an object is the same regardless of how far away it is from the napkin! That force is 2pi * G * m * rho where rho is the mass density of the napkin.

How is that possible since the force on a test particle on the surface of the napkin is 0?

Re: An Infinitely Large Napkin

#32

Post by galaxyLogic »

kangnkodos wrote: post #6
kangnkodos wrote: post #5

Earlier quoted context omitted.

Many, many years. Also, it's a thing in college. I don't think they talked about this much in high school when I was there. If they did, they started each book with a review, "Z is the set of integers".

I agree with you that for anyone who recently took math in college, it's obvious that Z is the set of integers. But for someone just learning it? Not so much.

I would say that even though it may be commonly used it is a bad name for Integers because it is not mnemonic. "I" would be a much better name for the set of Integers I would think.

But whatever you call it should not be too much effort to state in the beginning of a presentation or chapter or book, these are the symbols we will be using:

I = Set of Integers, ....

Sure it might be redundant but it is also easy for the reader to step over such explanations if they are familiar with them, but come back if they find some symbol they are not quite sure of. Question is are we trying to make the book easy for readers to understand, or short for the writer to write.

Re: An Infinitely Large Napkin

#34

Post by ginnungagap »

galaxyLogic wrote: post #32
kangnkodos wrote: post #6

Earlier quoted context omitted.

I agree with you that for anyone who recently took math in college, it's obvious that Z is the set of integers. But for someone just learning it? Not so much.

I would say that even though it may be commonly used it is a bad name for Integers because it is not mnemonic. "I" would be a much better name for the set of Integers I would think. But whatever you call it should not be too much effort to state in the beginning of a presentation or chapter or book, these are the symbols we will be using: I = Set of Integers, .... Sure it might be redundant but it is also easy for th…

It is a mnemonic if you're German, which is where the symbol comes from, it's the Z of Zählen!

Re: An Infinitely Large Napkin

#35

Post by matt_kantor »

todd8 wrote: post #14

I'm a computer scientist, not a mathematician (but I've taken around 25 college math courses spread over many years). Nevertheless, I do have a couple of suggestions and observations that I will address to the author that I hope is seeing this. First, it would be a very sophisticated high school student to tackle topology and some of the other areas of abstract mathematics. I really like the topics you've picked for…

> suggestions and observations that I will address to the author that I hope is seeing this

The author's site has a contact page (http://web.evanchen.cc/contact.html), you could send them your feedback directly.

Re: An Infinitely Large Napkin

#36

Post by Cerium »

fjsolwmv wrote: post #31
improv32 wrote: post #25

Earlier quoted context omitted.

Here's a cool link I just found going over this exact scenario: https://www.mathpages.com/home/kmath530/kmath530.htm Interesting to note, the napkin creates a uniform gravitational field above and below it. Meaning that the force applied to an object is the same regardless of how far away it is from the napkin! That force is 2pi * G * m * rho where rho is the mass density of the napkin.

How is that possible since the force on a test particle on the surface of the napkin is 0?

It is the same result as infinite planar light sources or infinite planar electrostatic charges. Move the test particle a small delta above or below the napkin, and the result will become apparent.

Re: An Infinitely Large Napkin

#37

Post by galaxyLogic »

ginnungagap wrote: post #34
galaxyLogic wrote: post #32

Earlier quoted context omitted.

I would say that even though it may be commonly used it is a bad name for Integers because it is not mnemonic. "I" would be a much better name for the set of Integers I would think. But whatever you call it should not be too much effort to state in the beginning of a presentation or chapter or book, these are the symbols we will be using: I = Set of Integers, .... Sure it might be redundant but it is also easy for th…

It is a mnemonic if you're German, which is where the symbol comes from, it's the Z of Zählen!

Good point. Of course. But if I'm writing or reading in English I still would prefer "I".
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