There are only 10 types of people in the world – those who understand binary, and those who don’t. And so the book starts with 'zeroth chapter' as 0 has a significant value.
Mathematics is a rapidly evolving field, Matt Parker here necessarily tries to remind us of that truth. This book operates as a tour bus for readers who want to learn more about a wide variety of mathematical topics and how it can be fun.
For instance, the number 111,111,111 multiplied by the same gives 12345678987654321 which is quite pleasing. Some more such tricks are added in the chapter. Another one which is quite interesting is 333. When these 3 digits are added, it gives 9. Dividing 333 by 9 gives 37 and this number results regardless of the digit we use. You can try with 888 and divide it by 24.
The author goes on to say that Mathematics is about adding new rules and see what happens on breaking them!
On the fun aspect to his narration we are asked to visit the website of NASA which host 'astronomy pictures daily- https://apod.nasa.go/htmltest.gifcity/sqrt2.1mil- and upon visiting you will be treated with "The Square Root of Two to 1 Million Digits". These digits are a whopping page consuming. Nevertheless, NASA says it is for fun and it really is.
One more fun you can try out is 3(3+1)x (2x3+1) / 6 = 14
With Paul Erdos commenting the discovery of the century as Ramanujan, an anecdote of an event in which mathematician Thomas Hardy visits an ailing Ramnujan is quoted. Thomas Hardy told Ramanujan that the taxi number in which he came was rather boring. It was 1729, to which Ramanujan quipped at once, "This is the smallest number which could be written as the sum of 2 cube numbers in 2 different ways". They are 9^3+10^3 and 1^3+12^3. The genius to the fore!
Parker also discusses the honeycomb conjecture and Thomas Hales. The honeycomb conjecture asks us to minimize the perimeter of a connected planar region, relative to its ability to cover the plane without overlap. There is this mention about why circular wheels rotate while square ones do not. In physics we have the answer based on friction which is minimum with circle. Here the author describes it circle geometry not allowing the change in centre of mass (while rotating). The CMS changes when it is square or any other shape and the illustration is very satisfying.
Quite common with puzzles is the pizza cutting in equal halves or other shapes. Parker illustrates them with so many shapes and divisions with constant width. For a regular polygon with odd number of sides one can flip just under half the edge inside and make corresponding polygon/folding or flexing.
This new thing called 'lune' can be witnessed if one draws two straight lines in the balloon. The kind of triangle one can make out from a sphere has also been the subject of discussion in Mario Livio's "Is God a Mathematician". Enough matter is there in the book for these parameters.
A strange question: Is it possible to fit an object through itself? (Say can you fit a cube through a hole in the cube of same size). Solved by Prince Rupert there is enough discussion on ways to slice a cube along with reference to the shadow of a cube which turns out to be hexagonal. Heard of Rupert's cube?
The discussion on Platonic solids is exhaustive too. The vertices, edges, faces, sides of several important shapes/geometries are well discussed. For a chemist this can assume significance as it can throw some light on to the crystal structure that just change name upon distribution of atoms. (like wurtzite and anti-wurtzite). The Octahedron has four triangles per vertex and icosahedron five.
The Herpes virus which was my guest last December finds a mention too, but only in terms of geometrical shape -Twenty icosahedron. These viruses just join the vertices to make a large structure which usually looks very beautiful. (we have been fed with so much on the present virus structure of 2020).
Also the bacteria are able to knot the DNA to make their population felt. If they are unable to unknot they cease to function! One of the best reference to this concept is the mathematical way to make the cancerous cells forget to knot! Makes out so much sense. If they forget to unknot they also might cease to function. How much mathematics has a role to play is quite appreciable.
About graph theory the author dedicates a chapter and cites a few books to read like "how to draw a straight line"- by Alfred Kempe!
When Kepler lost his wife he used statistical skill with mathematical model to find a new one and it took two years to get that. And it occurred to me that present data garnered by Facebook and Google can be used to achieve that goal in quite a square root time (of 2).
We usually associate pi with circular radius and other factors connected with circle. But here was a new thing : 1+1/4 +1/9+1.16 = Pi^2 /6. How does pi prop us suddenly here. The author leaves us to ponder over this question which is highly significant.
The last few chapters really made good reading with reference to Algorithm, Avicenna, Bernoulli, Mobuis (and Listing the discoverer of the strip but named after Mobius), Negative numbers etc. The author has set up a site to justify his book which is makeanddo4d.com
As promised in the title, the book gives us some things to make and do. Building a tesseract, a hyper cube, out of pipe cleaners and drinking straws might prove good for students who want to model them. There are also some fun ideas for knitted and crocheted mathematics. Many of the puzzles and creations are also available on the book's website if you don't want to cut up your book.
If you are a hesitant around mathematics, Parker has enough enthusiasm for you, and it is contagious.
