tizianocavigliablog

I post con tag "Pi Greco" archivio

Memorizzare le prime 200 cifre del Pi greco con un canzone

Wow   14.03.24  

Per celebrare il giorno del Pi greco, AsapSCIENCE ha composto una canzone per aiutarci a ricordare le prime 200 cifre della costante matematica che ha aperto la strada al mondo moderno.

3.14159 this is pi, followed by
2653589 circumference over di-ameter
7-9 then 323 o-m-g, can't you see?
8462643 and now we're on a spree

38 and 32 now we're blue, oh who knew!
7 thousand 9 hundred 50 and then 2
88 and 41, so much fun, now a run!
97 16939937 51 - halfway DONE

058 now don't be late, 209 where's the wine
7-4 it's on the floor, then 9-4-4-5-9
230 we gotta go, 78 we can't wait
1640628, we're almost near the end keep going

62 we're getting through, 089-9 on time
8628034 there's only a few more
8-2 then
5-3
42-11-7-0 and 67

We're done!
Was that fun?
Learning random digits so that you can brag to your friends

Are you ready for more?
We'll here's another hundred digits

98214 so many more
80865 let's all high five
13-282 well look at you
306 and your bag of tricks

6470 if you go slow
9-38-4 then you will score
4-6-0-9-5 now let's dive
505 into more pie

8 blue flying bats
Over 2 gold cats
23 shoes
172 screws

5 well dressed small dogs
Working 35 hour jobs

Oh this song
Is so absurd
Just rhyming pure random words

94081 can you taste your tongue?
28481 it just can't be done
117450 now close that door

Get those numbers in your brain
And keep them forevermore

284102
7-0 let's make a stew
1938521
105559 now our final run!

644-622
948 look at you
954-930
3819 and WOAH
The Pi Song 2.0

LEGGI ALTRO...

Il Pi greco e il concetto di infinito

Geek   14.03.19  
Le prime cifre decimali del Pi greco
Le prime cifre decimali del Pi greco

Nel suo libro di prossima uscita Infinite Powers: How Calculus Reveals the Secrets of the Universe, Houghton Mifflin Harcourt racconta come la costante Pi abbia aperto all'umanità la strada per familiarizzare e comprendere matematicamente il concetto di infinito.

Come proporzione, il Pi greco è stato usato fin dai tempi dei Babilonesi, ma fu il geometra greco Archimede, circa 2.300 anni fa, che per primo dimostrò come stimare rigorosamente il valore di pi. Tra i matematici del suo tempo, il concetto di infinito era tabù; Aristotele aveva cercato di bandirlo per essere troppo paradossale e logicamente infido. Nelle mani di Archimede, tuttavia, l'infinito divenne un cavallo di battaglia matematico.

Lo ha usato per scoprire l'area di un cerchio, il volume di una sfera e molte altre proprietà di forme curve che avevano messo in discussione i migliori matematici prima di lui. In ciascun caso, ha approssimato una forma curva utilizzando un gran numero di piccole linee rette o poligoni piatti. Le approssimazioni risultanti erano oggetti poligonali e sfaccettati che davano una visione fantastica delle forme originali, specialmente quando immaginava di usarne infiniti, con lati infinitesimamente piccoli nel processo.

Nel cercare di domare l'infinito Archimede ha aperto la strada al mondo moderno.

In ogni campo dello sforzo umano, dalla chirurgia plastica ricostruttiva alla simulazione dell'aria che scorre oltre l'ala di un jet, miliardi di minuscoli elementi discreti rappresentano una realtà intrinsecamente fluida e analogica. Tutto è iniziato con il calcolo di Pi. Il Pi greco rappresenta un limite matematico: un'aspirazione verso la curva perfetta, un progresso costante verso una stella irraggiungibile. Esiste, chiaro come la notte, senza una fine.

LEGGI ALTRO...

Il compleanno in Pi greco

Geek   14.03.17  

Nell'infinta sequenza di cifre del Pi Greco si possono scoprire innumerevoli altre sequenze di numeri come, ad esempio, il giorno del proprio compleanno.
Time ha creato un apposito script per facilitarci il compito e aiutarci a scovare dove si nasconde la nostra data di nascita.

LEGGI ALTRO...

Le cifre decimali del Pi greco che servono alla NASA

Geek   27.03.16  

I matematici sono arrivati a calcolare miliardi di cifre decimali del Pi greco, ma alla NASA hanno bisogno solo di 15 cifre decimali per esplorare l'intero sistema Solare. 3,141592653589793.

1. The most distant spacecraft from Earth is Voyager 1. It is about 12.5 billion miles away. Let's say we have a circle with a radius of exactly that size (or 25 billion miles in diameter) and we want to calculate the circumference, which is pi times the radius times 2. Using pi rounded to the 15th decimal, as I gave above, that comes out to a little more than 78 billion miles. We don't need to be concerned here with exactly what the value is (you can multiply it out if you like) but rather what the error in the value is by not using more digits of pi. In other words, by cutting pi off at the 15th decimal point, we would calculate a circumference for that circle that is very slightly off. It turns out that our calculated circumference of the 25 billion mile diameter circle would be wrong by 1.5 inches. Think about that. We have a circle more than 78 billion miles around, and our calculation of that distance would be off by perhaps less than the length of your little finger.

2. We can bring this down to home with our planet Earth. It is 7,926 miles in diameter at the equator. The circumference then is 24,900 miles. That's how far you would travel if you circumnavigated the globe (and didn't worry about hills, valleys, obstacles like buildings, rest stops, waves on the ocean, etc.). How far off would your odometer be if you used the limited version of pi above? It would be off by the size of a molecule. There are many different kinds of molecules, of course, so they span a wide range of sizes, but I hope this gives you an idea. Another way to view this is that your error by not using more digits of pi would be 10,000 times thinner than a hair!

3. Let's go to the largest size there is: the visible universe. The radius of the universe is about 46 billion light years. Now let me ask a different question: How many digits of pi would we need to calculate the circumference of a circle with a radius of 46 billion light years to an accuracy equal to the diameter of a hydrogen atom (the simplest atom)? The answer is that you would need 39 or 40 decimal places. If you think about how fantastically vast the universe is — truly far beyond what we can conceive, and certainly far, far, far beyond what you can see with your eyes even on the darkest, most beautiful, star-filled night — and think about how incredibly tiny a single atom is, you can see that we would not need to use many digits of pi to cover the entire range.

LEGGI ALTRO...

6 curiosità sul Pi greco

Geek   14.03.16  

6 curiosità sul Pi greco nel giorno del Pi greco.

There are many approximations for Pi

If you have a circle, you can measure two things: the distance around the perimeter of the circle (circumference) and the distance across the widest part of the circle (diameter). No matter how big your circle, the ratio of circumference to diameter is the value of Pi. Pi is an irrational number—you can't write it down as a non-infinite decimal. This means you need an approximate value for Pi.

The simplest approximation for Pi is just 3. Yes, we all know that's incorrect, but it can at least get you started if you want to do something with circles. In the past, many math books listed Pi as 22/7. Again, this is just an approximation but it is better than the value of 3 (actually 22/7 is closer to Pi than just writing 3.14).

The early history of mathematics covers many approximations of the value of Pi. The most common method would be to construct a many-sided polygon and use this to calculate the perimeter and diameter as an estimate for Pi. Other cultures found ways to write Pi as an infinite series—but without a computer, this can be sort of difficult to calculate out very far.

LEGGI ALTRO...

L'importanza del Pi greco

Geek   14.03.15  

I'm dreading it. No hope of solving any equations that day, what with the pie-eating contests, the bickering over the merits of pi versus tau (pi times two), and the throwdowns over who can recite more digits of pi. Just stay off the streets at 9:26:53, when the time will approximate pi to ten places: 3.141592653.

Pi does deserve a celebration, but for reasons that are rarely mentioned. In high school, we all learned that pi is about circles. Pi is the ratio of a circle’s circumference (the distance around the circle, represented by the letter C) to its diameter (the distance across the circle at its widest point, represented by the letter d). That ratio, which is about 3.14, also appears in the formula for the area inside the circle, A = πr2, where π is the Greek letter "pi" and r is the circle's radius (the distance from center to rim). We memorized these and similar formulas for the S.A.T.s and then never again used them, unless we happened to go into a technical field, or until our own kids took geometry.

So it's fair to ask: Why do mathematicians care so much about pi? Is it some kind of weird circle fixation?

Steven Strogatz sul nostro numero trascendente preferito nel giorno che lo celebra.

LEGGI ALTRO...