The never-repeating digits of `\pi` can be approximated by
22/7 = 3. 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!
There are two kinds of `\pi` Approximation Day posters.
The first uses the Archimedean spiral for its design, which I've used before for other numerical art. The second packs warped circles, whose ratio of circumference to average diameter is `22/7` into what I call `\pi`-approximate circular packing.
In the Approximation Day poster, all `m/n` rational approximations to `\pi` are shown as circles on a spiral. The circle at the start of the spiral (top) corresponds to `m=1`. The circle at the center of the spiral corresponds to `m=10000`.
Each circle is colored by the accuracy of the best possible approximation `m/n` according to the color scheme below, which is the legend inset. For example, for `m=22` the best approximation has `n=7`.
The accuracy cutoffs were selected to assign roughly the same number of points to each category.
The location of the best approximations within each accuracy window is shown below.
We focus on the important distinction between confidence intervals, typically used to express uncertainty of a sampling statistic such as the mean and, prediction and tolerance intervals, used to make statements about the next value to be drawn from the population.
Confidence intervals provide coverage of a single point—the population mean—with the assurance that the probability of non-coverage is some acceptable value (e.g. 0.05). On the other hand, prediction and tolerance intervals both give information about typical values from the population and the percentage of the population expected to be in the interval. For example, a tolerance interval can be configured to tell us what fraction of sampled values (e.g. 95%) will fall into an interval some fraction of the time (e.g. 95%).
Altman, N. & Krzywinski, M. (2018) Points of significance: Predicting with confidence and tolerance Nature Methods 15:843–844.
Krzywinski, M. & Altman, N. (2013) Points of significance: Importance of being uncertain. Nature Methods 10:809–810.
A 4-day introductory course on genome data parsing and visualization using Circos. Prepared for the Bioinformatics and Genome Analysis course in Institut Pasteur Tunis, Tunis, Tunisia.
Data visualization should be informative and, where possible, tasty.
Stefan Reuscher from Bioscience and Biotechnology Center at Nagoya University celebrates a publication with a Circos cake.
The cake shows an overview of a de-novo assembled genome of a wild rice species Oryza longistaminata.
The presence of constraints in experiments, such as sample size restrictions, awkward blocking or disallowed treatment combinations may make using classical designs very difficult or impossible.
Optimal design is a powerful, general purpose alternative for high quality, statistically grounded designs under nonstandard conditions.
We discuss two types of optimal designs (D-optimal and I-optimal) and show how it can be applied to a scenario with sample size and blocking constraints.
Smucker, B., Krzywinski, M. & Altman, N. (2018) Points of significance: Optimal experimental design Nature Methods 15:599–600.
Krzywinski, M., Altman, N. (2014) Points of significance: Two factor designs. Nature Methods 11:1187–1188.
Krzywinski, M. & Altman, N. (2014) Points of significance: Analysis of variance (ANOVA) and blocking. Nature Methods 11:699–700.
Krzywinski, M. & Altman, N. (2014) Points of significance: Designing comparative experiments. Nature Methods 11:597–598.
An illustration of the Tree of Life, showing some of the key branches.
The tree is drawn as a DNA double helix, with bases colored to encode ribosomal RNA genes from various organisms on the tree.
All living things on earth descended from a single organism called LUCA (last universal common ancestor) and inherited LUCA’s genetic code for basic biological functions, such as translating DNA and creating proteins. Constant genetic mutations shuffled and altered this inheritance and added new genetic material—a process that created the diversity of life we see today. The “tree of life” organizes all organisms based on the extent of shuffling and alteration between them. The full tree has millions of branches and every living organism has its own place at one of the leaves in the tree. The simplified tree shown here depicts all three kingdoms of life: bacteria, archaebacteria and eukaryota. For some organisms a grey bar shows when they first appeared in the tree in millions of years (Ma). The double helix winding around the tree encodes highly conserved ribosomal RNA genes from various organisms.
Johnson, H.L. (2018) The Whole Earth Cataloguer, Sactown, Jun/Jul, p. 89
An article about keyboard layouts and the history and persistence of QWERTY.
McDonald, T. (2018) Why we can't give up this odd way of typing, BBC, 25 May 2018.