Posts Tagged ‘math’

Happy Pi Day 2016!

Has it really been a whole year?

On Pi Day 2015 hack-r.com posted a tribute to Pi (π) Day, published on GitHub, wherein we created fractals in R based on π, scraped and displayed information on Pi and other fun stuff.

This year, find out how Fibonacci numbers, which are sequences of integers, have a freaky relationship with π! View the entire script on GitHub.


# Pi Fibonacci Sequence ---------------------------------------------------
cat("This year, we'll look at the relationship between Pi and Fibonacci sequences. \n")
cat("Until very recently there were just two methods used to compute pi (π),
one invented by the Greek mathematician Archimedes,
and the other by the Scottish mathematician James Gregory. \n")

cat("If we use Sir Gregory's arc tangent method, you'll notice a pattern...")

pi/4
atan(1)

pi/4 == atan(1)

atan(1/3)
atan(1/5)  + atan(1/8)

atan(1/8)
atan(1/13) + atan(1/21)

cat("We can combine what we saw above")
pi/4
atan(1/2) + atan(1/3)
atan(1/2) + atan(1/5) + atan(1/8)

atan(1/21)
atan(1/34) + atan(1/55)

cat("You'll notice that the pattern is a Fibonacci sequence! \n")

cat(" We have just seen that there are infinitely many formulae for π using the Fibonacci numbers!")

pi

R: Happy Pi Day

Today, 3/14/2015, is Pi Day (see http://piday.org).

In honor of Pi Day, I threw together a little R code on Github, which discusses pi, prints it, and creates Julia set (fractal) images based on it:

https://github.com/hack-r/Rpiday

Happy Pi Day!

pi_fractal

Stats: Moments

Significance of moments (raw, central, standardised) and cumulants (raw, standardised), in connection with named properties of distributions
Moment numberRaw momentCentral momentStandardised momentRaw cumulantStandardised cumulant
1mean00meanN/A
2variance1variance1
3skewnessskewness
4historical kurtosis (or flatness)modern kurtosis (i.e. excess kurtosis)
5hyperskewness
6hyperflatness
7+