Mathematics is dirty about the edges. It only appears **** and span.


So the word sp*c (* =i) is removed from the 2+2 lexicon. So be it.

So change the definition of a circle. Have it that some circles are more circular than others, like IRL, and let perfect circles be a limiting case, for the weirdos to get excited about.

1. Get a thesaurus.
2. Look up ‘fighting words’ in an unabridged encyclopedia.
3. ??!?
4.Profit in knowledge.

Pi competition starting now. Provide the quickest estimate or plan that is done within 1hr by hand (no calculators or computers allowed) for Pi using geometry you can imagine. Like pretend you never knew any digits of Pi and wanted to get as many as possible fast with simple arguments. Dont give me any wikipedia bs with Ramanujan sums etc unless you can prove it fast. Calculus is in it too if you can think a quick way there.

Put a square outside and inside the circle, sides and corners touching the circle. First the outside one: the diameter of the circle is one fourth of the circumference of the square. So pi is less than 4. Then the inside one: use the Pythagorean theorem. Pi has to be bigger than 4 divided by the square root of 2 ~= 2.83.

So I'd say pi iz zomewhere between 2.83 and 4.

You could try using a pentagram to narrow down your range a bit

Yes. He did use a particular method.

LOL digitaments

3 is a stupid number. Don't memorize it. There's so many more important efforts to engage your brain cells.

In his mind, Tammet says, each*positive integer*up to 10,000 has its own unique shape, colour, texture and feel. He has described his visual image of 289 as particularly ugly, 333 as particularly attractive, and*pi, though not an integer, as beautiful. The number 6 apparently has no distinct image yet what he describes as an almost small nothingness, opposite to the number 9 which he calls large, towering, and quite intimidating. He also describes the number 117 as "a handsome number. It's tall, it's a lanky number, a little bit wobbly".

Sent from pickle redia

The numbers 1-100 go up like the right side of a parabola from 1 to 10, then go up curving back to the left from 10-20, then go straight up from 20-30, then curve back to the right in S fashion from 30-75, then back to the left from 75-100. That's how it's been since I first learned to count and as far as I'm concerned that's how it is.


PairTheBoard

You probably mean regular pentagon.

This is what I got when I asked google for the meaning of pentagram. The "Enter a word" phrase is in a search box.
-----------------
Dictionary

Enter a word, for e.g. "pie"


pen·ta·gram
ˈpen(t)əˌɡram/
noun
noun: pentagram; plural noun: pentagrams
a five-pointed star that is formed by drawing a continuous line in five straight segments, often used as a mystic and magical symbol.
================


Spooky.


PairTheBoard

There's one on the flags of Morocco and Ethiopia.

Interesting.

I probably did

Paying homage to my great predecessors w/o Pi feels so empty.

Here is my best method so far, still working on other ideas. (use Desmos to visualize the next plotting relevant curves https://www.desmos.com/calculator)

Consider the circle x^2+(y-1)^2=1 and the parabola y=1/2*x^2. Then consider a=((1-3^(1/2)/2))/2)^(1/2) (that is sine of Pi/12 basically ie 15 deg, you can get that from the double angle trigonometric identity formula).

Because the parabola approximates very well the curve of the circle from -a to a (do Taylor expansion of the circle curve to see why), the area of the rectangle with dimensions 2a*1 is equal to the circular section Pi/12 plus the two triangles 2*1/2*a*(1-a^2)^(1/2) plus the area below the parabola from -a to a that is 1/3*a^3.

eg see here all this

https://www.desmos.com/calculator/42s4uakype

zoom https://www.desmos.com/calculator/smwzcimika


Since one can calculate square roots of eg K easily with the sequence x_(n+1)=1/2(x_n+K/x_n)

one can use the above to get Pi~3.1423 that beats 22/7 by my countryman Archimedes lol. Probably done within less than 2-3 hours without calculator assistance on the square roots.

One can improve on that going to 7.5 degrees even with a=0.130526192 and then get 3.1416 hehe!
Go for 3.75 degrees and it gets to 3.141596. All this doable within 4h of math using the rational approximation of square roots above that converges fast.

He could obtain this result by the way because he knew what the area below a parabola is with other methods than calculus but its too tough to ask for such long time ago in a world without paper and more compact symbols formalism for the algebra.

One can also use as fit for the circle the 4th order polynomial y=1/2*x^2+1/8*x^4 that approximates even better the circle and can yield the easy result with only even a= sine15 calculation with radicals a result as great as 3.1415929 vs the real thing 3.1415927 that is off by only 1 part in 10 mil or so.

If one goes completely crazy and approximates the circle using

y=x^2/2 + x^4/8 + x^6/16 + 5 x^8/128

then with a=sin15=((1-3^(1/2)/2))/2)^(1/2)

yields a ridiculous good result like 3.14159266 vs the real thing 3.14159265 off by only 1 part in 500 mil. You can probably do this without computer in a day.

Ha, regarding you know who...

Real power is not fear.

Real power is the final love and respect from your opponents when they are happily not your enemies anymore, as ethical intellect has finally proven victorious over fear and insecurity on the way to a new world where all sides have grown wiser!

Fear had it’s usefulness before when we really needed it to survive in our ecosystem. Now it is totally unnecessary- yet still used, and has become a huge burden of artificial limits and as an impetus for violence. I agree, Love is a better choice, an upgrade from fear, fit for adaptability and progress in our present ecosystem. Fear-mongers can barely scratch the surface of a mind, aware of fear, which takes action and loves.

I'm forming an elite club for elitists for the mutual celebration of our elitism. Parties will be catered by Domino's Pizza. BYOB.


PairTheBoard

Will feel the freedom of not joining