Archive for the ‘Math’ Category

Happy Pi Day 2018!

In honor of Pi Day, I usually like to do a little on-topic code snippet.

This year I was running low on time, but I thought I’d ask the question “Can Pi be useful in predictive modeling, ML, AI, etc?”.

Of course the answer is going to be a big “yes!”. Transformations with natural numbers are underutilized, perhaps because it’s not always intuitive to leverage a constant scalar in a model. Let’s see a trivial example with the famous `iris` data set, built into R.

Compare the 2 models below and you’ll be pleasantly surprised. Pi helped us explain more variance and helped to create another highly significant predictor capturing a potentially unique effect:

data(iris)

summary(lm(I(iris$Species=="setosa") ~ iris$Sepal.Length, data = iris))
summary(lm(I(iris$Species=="setosa") ~ iris$Sepal.Length + I(iris$Sepal.Length^pi), data = iris))

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