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`\pi` Approximation Day Art Posters
The never-repeating digits of `\pi` can be approximated by 22/7 = 3.142857 to within 0.04%. These pages artistically and mathematically explore rational approximations to `\pi`. This 22/7 ratio is celebrated each year on July 22nd. If you like hand waving or back-of-envelope mathematics, this day is for you: `\pi` approximation day!
getting it mostly right
Curiously, the 22/7 rational approximation of `\pi` is more accurate (to within 0.04%) than using the first three digits 3.14, which are accurate to 0.05%.
It seems that `\pi` Approximation Day is 20% more accurate (verify on Wolfram Alpha)! And therefore definitely worth celebrating. $$ \frac{(\pi-3.14)-(22/7-\pi)}{\pi-3.14} = 0.206 $$
art of `\pi` rational approximation
The poster shows the accuracy of 10,000 rational approximations of `\pi` for each `m/n` and `m=1...10000`. Read about the details of the method.
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art of `\pi`-approximate packing
These posters show warped circles, which embody the 22/7 approximation of `\pi`, using a retro 1970's color scheme. Read about the details of the method.
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news + thoughts
Happy 2021 `\pi` Day—
A forest of digits
Celebrate `\pi` Day (March 14th) and finally see the digits through the forest.
This year is full of botanical whimsy. A Lindenmayer system forest – deterministic but always changing. Feel free to stop and pick the flowers from the ground.
And things can get crazy in the forest.
Check out art from previous years: 2013 `\pi` Day and 2014 `\pi` Day, 2015 `\pi` Day, 2016 `\pi` Day, 2017 `\pi` Day, 2018 `\pi` Day and 2019 `\pi` Day.
Testing for rare conditions
All that glitters is not gold. —W. Shakespeare
The sensitivity and specificity of a test do not necessarily correspond to its error rate. This becomes critically important when testing for a rare condition — a test with 99% sensitivity and specificity has an even chance of being wrong when the condition prevalence is 1%.
We discuss the positive predictive value (PPV) and how practices such as screen can increase it.
Altman, N. & Krzywinski, M. (2021) Points of significance: Testing for rare conditions. Nature Methods 18
Standardization fallacy
We demand rigidly defined areas of doubt and uncertainty! —D. Adams
A popular notion about experiments is that it's good to keep variability in subjects low to limit the influence of confounding factors. This is called standardization.
Unfortunately, although standardization increases power, it can induce unrealistically low variability and lead to results that do not generalize to the population of interest. And, in fact, may be irreproducible.
Not paying attention to these details and thinking (or hoping) that standardization is always good is the "standardization fallacy". In this column, we look at how standardization can be balanced with heterogenization to avoid this thorny issue.
Voelkl, B., Würbel, H., Krzywinski, M. & Altman, N. (2021) Points of significance: Standardization fallacy. Nature Methods 18:5–6.
Graphical Abstract Design Guidelines
Clear, concise, legible and compelling.
Making a scientific graphical abstract? Refer to my practical design guidelines and redesign examples to improve organization, design and clarity of your graphical abstracts.
"This data might give you a migrane"
An in-depth look at my process of reacting to a bad figure — how I design a poster and tell data stories.
He said, he said — a word analysis of the 2020 Presidential Debates
Building on the method I used to analyze the 2008, 2012 and 2016 U.S. Presidential and Vice Presidential debates, I explore word usagein the 2020 Debates between Donald Trump and Joe Biden.
