The Meditations in this book are the product of thousands of years of mathematical discourse. As you read through the book and work through the various exercises, you will discover new mechanisms that allow you to contemplate and understand some complex mathematical principles.
Mathematical Meditations identifies, explores, and celebrates those aspects of mathematics that are good for you and your overall wellbeing. It is necessary for everyone to have a little time to think every so often: to contemplate, meditate, and try to understand where you are and what is going on around you. Mathematics can help you with all of that.
The Meditations in this book are the product of thousands of years of mathematical discourse. As you read through the book and work through the various exercises, you will discover new mechanisms that allow you to contemplate and understand some complex mathematical principles. However, the focus will always be wider than a mere dry comprehension of theory, as you will be encouraged to meditate upon the deeper intrinsic beauty of mathematics and what it can reveal to us about the world around us.
Features
- An original, engaging narrative format replete with novel exercises and examples
- Could be used in a classroom setting for liberal arts students, mathematics undergraduates, or high school teachers
- Accessible to anyone who wants to explore a different kind of perspective on mathematics
1. Labyrinth: From Minotaur to Chartres. The Cretan Labyrinth. The
Labyrinth of the Notre Dame de Chartres. Further Exploration.
2. Pathways and
Bridges. The Famous Seven Bridges. Further Doodling with Pathways. The
Inspector General. Closing of the Pathways with Hamilton. Further
Exploration.
3. Diagrams to Contemplate Upon. The Right-Angled Triangle with
an Inscribed Square. The Mean Proportional. Now for the Circles. Signs by the
Roadside on a Shinto Pilgrimage. Little Meditative Question from Dyson.
Further Reading.
4. Music for Your Mind. Bach, the Art of Fugue, and Group
Theory. Our Tool Set Group Theory. Applying Group Theory to Music. The
Musical Clock. Further Exploration.
5. Friendships: Mathematicians and
Musicians. Gersonides and the Free Will Question. Further Exploration.
6.
Presence and Transience. Crome or Chrome, Huxleys Yellow. Sketching with the
Chrome Yellow. The Numbers that Keep Coming Up. Further Exploration.
7.
Prussian Blue and the Blue Waves. The Wave and the Fractals. A Group of
Mathematicians of Order Three. What Does B in Benoit B. Mandelbroth Stand
For? Fractal Making. The Ideal Library. Further Exploration.
8. Que Sera,
Sera (What Will Be Will Be). The Dreams and Dreamers. Harmony of the World.
Beautiful Solids. Further Exploration.
9. Questions and Answers. Goldbach
Conjecture. Twin Prime Conjecture. 196-Algorithm. Is 10 a Solitary Number?.
Further Investigations.
10. The Centre of Action. It Is Elementary, My Dear
Miss Watson. A Few Other Circles. The Excircles. Some Points on (All)
Circles. Further Explorations.
11. Mathematical Objects. Arithmetica by
Diophantus. Hilberts Hotel. Möbius Band. Piero della Francescas
Masterpiece? Further Reading.
12. Tracing the Movement. Imagine a Trace You
Leave Behind. Hyperbolas and Ellipses in Motion. Dandelins Ice Cream.
Further Explorations.
13. Mathematicians Alicia Boole Stott (18601940).
Viggo Brun (18851978). Germinal Dandelin (17941847). Diophantus (date of
birth unknown? 284 AD). Freeman Dyson (19232020). Euclid. Leonhard Euler
(17071783). Pierre Fatou (18781929). Pierre de Fermat (16011665). Karl
Wilhelm Feuerbach (18001834). Rene Maurice Fréchet (18781973). Gersonides
(12881344). Christian Goldbach (16901764). Alexander Grothendieck
(19282014). William Rowan Hamilton (18051865). David Hilbert (18621943).
Hypatia (c.350415). Iamblichus (c. 245c.325). Gaston Julia (18931978).
Fuijita Sadasuke Kagen (17341821). Johannes Kepler (15711630). Felix
Christian Klein (18491925). Gottfried Wilhelm Leibniz (16461716). Paul
Pierre Lévy (18861971). Benoit B. Mandelbrot (19242010). Marin Mersenne
(15881648). August Ferdinand Möbius (17901868). Gaspard Monge (17461818).
Nicomachus (c. 60c. 120). Nicole Oresme (13251382). Blaise Pascal
(16231662). Louis Poinsot (17771859). Pythagoras of Samos (c. 570 BCEc.
495 BCE). Bertrand Russell (later Lord Russell, 3rd Earl Russell, 18721970).
Theon of Smyrna (flourished around 100). Ernst Zermelo (18711953). Post
Scriptum and All That
Snezana Lawrence is a mathematical historian and mathematics educator, and has been working in higher education for the past 15 years. Prior to that, Snezana was a teacher and teacher trainer in the English school-system. She was a lead consultant for the Princes Teaching Institute for Mathematics 2009-2018. Currently Snezana works as a Senior Lecturer in the Department of Mathematics and Design Engineering at Middlesex University, London, teaching mathematics, mathematics history, and risk.
Snezanas plan for the next few years it to write more popular history of mathematics books and to work more with teachers and people interested in identifying their local history of mathematics in libraries and museums where they live, across Europe. She was the Chair of the History and Pedagogy of Mathematics International Study Group for 2020-2024.
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