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The sometimes 'Beauty' of mathematics???
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RJSV:
(continued).
... Getting schetchy here, but my inclination is to set up, maybe TWO 'simultaneous' equations. Having a diameter D1 and a later diameter D2.
You already have C1 and C2 (C2 is just 1 meter larger).
   At this point, realize that we need, one of those MATH types, here.
mathsquid:
Let \$r\$ be the radius of the earth. Put a rope around the earth at the equator to get a circle. Its circumference is \$2\pi r\$. Now take another rope that is one meter longer, and use it to make a circle that is \$a\$ meters above the earth.

Since the longer rope is one meter longer, the circumference of the bigger circle is \$ 2 \pi r + 1\$.

The radius of the bigger circle is \$r + a\$, thus the circumference of the bigger circle is \$2\pi (r+a) \$

Together we have
$$2 \pi r + 1 = 2\pi (r+a)$$
$$2 \pi r + 1 = 2\pi r + 2\pi a$$
$$ 1 =  2\pi a$$
$$ a = \frac{1}{2 \pi}$$
mawyatt:
Using a little elementary calculus.

C = 2piR

dC = 2pi*(dR)

delta C = 2pi*(deltaR)

So the change in circumference wrt the change in radius is independent of the radius!!!

Thus the comment, about using the Earth, Moon, Jupiter, Solar System and Universe on one extreme, and a beachball, basketball, baseball, pingpong ball and atom on the other.

Best,
basinstreetdesign:

--- Quote from: The Electrician on August 05, 2021, 11:17:07 pm ---
--- Quote from: GlennSprigg on August 04, 2021, 01:48:17 pm ---I don't know how many people have seen my 'Tag' (?) thing, at the bottom of my posts/replies?   :P
   Diagonal of 1x1 square = Root-2. Ok.
   Diagonal of 1x1x1 cube = Root-3 !!!  Beautiful !!

Doesn't that not strike people as mathematically amazing! that the internal diagonal of a 'Cube' (1x1x1) = Root-3 !!!
I love the natural relationships with certain numbers, that can easily be proven/shown, and be so simple!   8)
GREAT!!  Good-ol basic maths can show/prove it all !!!...

Then I found out recently, that there is NO KNOWN correct formula, to calculate the Circumference of an 'Ellipse' !!   :palm:
You don't believe it... then look it up!!  Sigh...   Just lost faith in Maths again...   :box:

--- End quote ---

Of course there is a correct formula.  The relevant observation is found on this page: http://www.numericana.com/answer/ellipse.htm#elliptic

"There is no simple exact formula:  There are simple formulas but they are not exact, and there are exact formulas but they are not simple."

Also here: https://wj32.org/wp/2012/12/15/formula-for-the-circumference-of-an-ellipse/

--- End quote ---

I'm surprised that no one has mentioned that a simple extension of your sequence is that the "diagonal" (space-diagonal) of a 1 x 1 x 1 x 1 hypercube or tesseract is root(4) = 2
RJSV:
Magic and Mathsquid:
   Just so I can sleep tonight:.       1/ 2 * pi
ntimeters
So that mouse has easy time, right ?  That's  around 6 inches of clearance, right ? Uhh 20 centimeters ?
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