NOTE: I took this as a 30 day challenge and I am glad I was able to see it through. It was fascinating and a great learning experience for me. I am now discontinuing this effort to pursue a couple of other ideas. Stay tuned!
“To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature … If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in. She offers her information only in one form; we are not so un-humble as to demand that she change before we pay any attention ” - Richard Feynman
A friend jokingly asked me if calculus is indeed used in everyday life beyond 12th-grade exams. This got me thinking, and as a personal endeavor to make mathematics fun and approachable, I am consolidating a list where mathematics gives more insight. The objective is to make people appreciate the use of mathematics in seemingly random applications in their everyday lives.
GROUND RULES:
- I will be referencing documents that are freely available online that anyone without institutional access/subscription can download and read. The credit goes to the brilliant scientists/authors of the journal/article/publication. I do NOT claim any credit for their work. The point is to make the reader appreciate the beauty of maths by pointing to their work. References follow and links in colour.
- I will not be making an effort to explain the complexities of the equations but rather show how mathematics is used in everyday applications. There could be conflicting works in the same domain, but I will make an effort to point to the seminal work in the area. References and citations can be tracked for latest developments in that area.
So let’s make mathematics fun?
02/05/2021
Phyllotaxis is the arrangement of leaves in a stem of a plant. It turns out that there is a mathematical model to recreate the pattern called the DC2 equation but with certain assumptions causing the model to fail for different plant types. The modified version of the equation has now been determined that is more general for all plant types.
References
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Douady, Stephane, and Yves Couder. Phyllotaxis as a physical self-organized growth process. Physical review letters 68.13 (1992): 2098. Link
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Yonekura, Takaaki, et al. Mathematical model studies of the comprehensive generation of major and minor phyllotactic patterns in plants with a predominant focus on orixate phyllotaxis.” PLoS computational biology 15.6 (2019): e1007044. Link
01/05/2021
Mathematical modelling of spatial settlements, human behavior in the past and its relationship between the physical structure of space and the quality of life forms the basis of computational archeology.
References
- Dettlaff, Weronika. Space syntax analysis–methodology of understanding the space. PhD Interdisciplinary Journal (2014): 283-291. Link
- Space Syntax Laboratory, University College, London Link
30/04/2021
Applied mathematics for social causes. This is a broad documentation released as a special issue, containing eleven different ideas on how differential equations can be used for social justice and environmental causes.
References
- Linking Differential Equations to Social Justice and Environmental Concerns - CODEE Online Journal Link
29/04/2021
What is the relationship between hill inclination, time and hiking speed required to climb a hill? Tobler’s hiking function gives precisely that, although the model was derived using emperical data.
References
- Tobler, Waldo. “Three presentations on geographical analysis and modeling.” (1993). Link
- Open source tool to compute the walking time Link
28/04/2021
What is so unique about the following jokes?
What is the difference between a pretty glove and a silent cat? - One is a cute mitten, the other is a mute kitten.
What do you call a strange market?- A bizarre bazaar
These punning riddles were created by a computer program called JAPE, and are a part of computational humour. This field uses mathematics, linguistics and AI to computationally model a sense of humour.
References
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Ritchie, Graeme. “The JAPE riddle generator: technical specification.” Institute for Communicating and Collaborative Systems (2003). Link
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Ritchie, Graeme, et al. “A practical application of computational humour.” Proceedings of the 4th International Joint Conference on Computational Creativity. (2007) Link
27/04/2021
Geometry and Origami (the art of paper folding) go hand-in-hand and is known to have applications in a variety of real-world problems. For example, the folding of paper can be used to determine the roots of a cubic equation. There is also an interesting connection between the art and an Indian Mathematician, T. Sundara Row (or Rao). He published Geometric exercises in Paper Folding in 1893, and is considered to be “one of the main engines of the popularization of folding as a mathematical activity” according to mathamatical historian Michael Friendman.
The book according to T. S. Rao was “..sought not only to aid the teaching of geometry in schools and colleges, but also to afford mathematical recreation to young and old, in an at- tractive and cheap form. “Old boys” like myself may find the book useful to revive their old lessons, and to have a peep into modern developments which, although very interesting and instructive, have been ignored by university teachers.”
References
- Rao, Tandalam Sundara, Geometric Exercises in Paper Folding. Open court pub. Company, 1901. Online Book
- Robert Lang Origami Website (He is considered to be a pioneer in the use of mathematics and engineering principles inspired by origami)
- Mathologer - Why don’t they teach this simple visual solution? (Lill’s method)
26/04/2021
The best way to lace your shoes mathematically.
References
Polster, B. What is the best way to lace your shoes?. Nature 420, 476 (2002) Link
25/04/2021
Taking a sofa round a corner? Pivot! Pivot! Pivot! Sorry, couldn’t help referencing Friends (Season 5, Episode 16) here :-)
“What is the planar shape of maximal area that can be moved around a right-angled corner in a hallway of unit width?” - The moving sofa problem
References
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Romik, Dan. “Differential equations and exact solutions in the moving sofa problem.” Experimental Mathematics 27.3 (2018): 316-330. Link
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The Moving Sofa Problem - Numberphile
24/04/2021
It is known that the wave equation, a class of partial differential equations, is one of the widely used equations to describe systems whose solutions are “wave” like, and is best used to study the vibration in a string, e.g. the plucking of a guitar string.
But do you know that the mathematical modelling of vibrating string led to a major controversy between d’Alembert, Euler and Daniel Bernouilli, beginning in 1750 and lasting 80 years until Fourier and Dirchilet provided a solution?
References
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Wheeler, Gerald F., and William P. Crummett. “The vibrating string controversy.” American Journal of Physics 55.1 (1987): 33-37 Link
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Zeeman, E. C. “Controversy in science: on the ideas of Daniel Bernoulli and René Thom.” Nieuw Arch. Wisk 11 (1993): 257.Link
23/04/2021
How to find a needle in a haystack?
References
- Craswell, Keith J. “How to Find a Needle in a Haystack.” The Two-Year College Mathematics Journal 4.3 (1973): 18-21.Link (Unfortunately requires institutional/subscription based login.)
22/04/2021
Marriage, Set theory and combinatorics?
References
- Hall’s Marriage Theorem, Brilliant.org, Retrieved 08:32, April 22, Link
- Fables of Data Science — Hall’s Marriage Theorem, Medium.com, Retrieved 08:35, April 22, Link
21/04/2021
Let’s go to space. Do extra-terrestrial, alien society exist and how many are detectable? Turns out this can be estimated using Drakes Equation, albeit with uncertainities.
References
20/04/2021
Say a new product is introduced in a market. How does it get adopted in a population and what is its sales prediction?
References
- Bass, Frank M. “A new product growth for model consumer durables.” Management science 15.5 (1969): 215-227. Link-1, Link-2
PS: It is one of the most highly cited work in management sciences!
19/04/2021
Getting into Operations Research, Logistics and Fleet management to find optimal routes for vehicles when visiting multiple set of locations. The seminal work in the area was called the “The Truck Dispatching Problem”, which later became, what is now known as, “Vehicle Routing Problem (VRP)”. This is a slightly complicated version of The Travelling Salesman problem discussed on 13/04/2021.
References
- Dantzig, George B., and John H. Ramser. “The truck dispatching problem.” Management science 6.1 (1959): 80-91. Link
- Google OR Tools - Vehicle Routing Problems Link (Follow the link for some really cool examples)
18/04/2021
In to the world of mathematical optimization. One very interesting application is use of multiobjective optimization techniques for Municipal Solid Waste Management Systems in cities.
References
- Sudha, Goel. “Municipal solid waste management (MSWM) in India a critical review.” J Environ Sci Eng 50.4 (2008): 319-328.Link-1 Link-2
- Chinchodkar, K. N., and Omprakash S. Jadhav. “Development of mathematical model for the solid waste management on dumping ground at Mumbai for the reduction of existence cost.” International Journal of Statistics and Systems 12.1 (2017): 145-155. Link
16/04/2021
Diving in to Botany. Mathematical modelling and plant growth analysis.
References
- Hunt, R., et al. “A modern tool for classical plant growth analysis.” Annals of botany 90.4 (2002): 485-488. Link
- Evans, George Clifford. The quantitative analysis of plant growth. Vol. 1. Univ of California Press, 1972.
15/04/2021
Differential equations to model interactions between two species, where one is a predator and other is a prey.
References
- Frank Hoppensteadt (2006) Predator-prey model. Scholarpedia, 1(10):1563. Link
14/04/2021
Mathematically modelling a modern war. Fun fact, chimpanzees intuitively follow this before engaging into a fight with another troop of chimpanzees.
References
- Bellany, Ian. “Modelling war.” Journal of peace research 36.6 (1999): 729-739.Link
- Wilson, Michael L., Nicholas F. Britton, and Nigel R. Franks. “Chimpanzees and the mathematics of battle.” Proceedings of the Royal Society of London. Series B: Biological Sciences269.1496 (2002): 1107-1112. Link
- Stanescu, Marius, Nicolas Barriga, and Michael Buro. “Using Lanchester attrition laws for combat prediction in StarCraft.” Proceedings of the AAAI Conference on Artificial Intelligence and Interactive Digital Entertainment. Vol. 11. No. 1. 2015. Link
13/04/2021
Finding a shortest possible route to nearly every pub in the UK.
References
- William Cook et al. Shortest possible tour to nearly every pub in the United Kingdom- UK49687 Link (Follow the link for some really cool explanations and other applications)
- Wikipedia - Travelling Salesman Problem Link
12/04/2021
There is a theorem to represent the seam of a tennis ball!
References
- Wikipedia - Tennis ball theorem. Link
- Curve described by a seam line of a tennis ball Link
- Math Stack Exchange is sometimes a great source of information Link-1, Link-2
- Parameteric equation of tennis ball seam curve
Additional: Aerodynamics of a tennis ball
- Alam, F., Subic, A., Naser, J., Rasul, M., & Khan, M. (2008). A study of spin effects on tennis ball aerodynamics Link
11/04/2021
What has Microsoft’s Minesweeper game got to do with the biggest unsolved problems in Computer Science?
References
- Richard Kaye’s Minesweeper Pages Link
- Ian Stewart on Minesweeper Link
- Claymath - P vs NP Problem Link
- P vs NP, The biggest unsolved problem in Computer Science - Up and Atom
10/04/2021
Will you change your mind, if I present you with a new fact? Delving in to the world of Bayesian Inference.
References
- Weisstein, Eric W. “Bayes’ Theorem.” From MathWorld–A Wolfram Web Resource. Link
- Arbital Guide to Bayes rule Link
- A Visual Guide to Bayesian thinking - Julia Galef
- The Bayesian Trap - Veritasium
09/04/2021
Checkmate! In the fascinating world of Chess, Graph theory to represent all the legal moves of a chess piece on a chess board.
References
- Wagon, Stan and Weisstein, Eric W. “Rook Graph.” From MathWorld–A Wolfram Web Resource. Link
- Bishop Graph Link
- Queen Graph Link
- King Graph Link
08/04/2021
“Psst! Aliens from Mars are amongst us. They are on a secret mission to take over our planet. Spread the word around”. Modelling rumour spread in a community using Logistic Differential Equation
References
- Weisstein, Eric W. “Logistic Equation.” From MathWorld–A Wolfram Web Resource. Link
- Class notes of Prof. Grant B. Gustafson, University of Utah Link
07/04/2021
Cooking that perfect egg.
References
06/04/2021
- The calculus that is used in modelling election voting and understanding political behaviour
References
Riker, W. H., & Ordeshook, P. C. (1968). A Theory of the Calculus of Voting. The American political science review, 62(1), 25-42. Link
05/04/2021
Thiele Differential Equation - The mathematics used in insurance products.
References
- Thiele differential equation. Encyclopedia of Mathematics. Link
04/04/2021
When zombies attack, we are screwed! Proof by mathematics.
Just kidding, the equations used are the same ones used to model an infection outbreak.
References
- Munz, P., Hudea, I., Imad, J., & Smith, R. J. (2009). When zombies attack!: Mathematical modelling of an outbreak of zombie infection. Infectious disease modelling research progress, 4, 133-150. Link
03/04/2021
How do you model a love-affair between 2 people? The maths behind love.
References
- Steven H. Strogatz (1988) Love Affairs and Differential Equations, Mathematics Magazine, 61:1, 35. Link, DOI