Book: Experimental Mathematics

Matemáticas experimentales is a mathematics outreach book published in the Estímulos Matemáticos collection, jointly edited by the Royal Spanish Mathematical Society (RSME) and SM.

Through hands-on, visual and interactive activities, the book offers a different way of approaching mathematics, connecting fundamental concepts with practical experiences that encourage curiosity, exploration and discovery.

Matemáticas Experimentales

Author: Francisco Javier Falcó Benavent

Publisher: Ediciones SM / RSME - Estímulos Matemáticos collection

Year: 2022

ISBN: 978-8413929293

Summary:
In elementary mathematics, hands-on activities are strongly integrated into teaching because they help students visualize and understand concepts. In advanced mathematics, however, their presence becomes much more limited.

In this book we rediscover five key mathematical theories whose definitions and results are complemented by applications to everyday situations and teaching proposals that allow us to see and touch the mathematical world.

As mathematician Stanley Gudder wrote, “The essence of mathematics is not to make simple things complicated, but to make complicated things simple.” In that same spirit, this book aims to turn complex abstractions into accessible knowledge.

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Complementary material

1. Conic sections and planetary orbits

• Conic section constructions
• 3D animated short film Ellipses by Pavel Boytchev
• Scale model of the solar system (PDF)
• Planet cards: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune

2. Graphs and connections: where less is more

• Paper trails (representing graphs with pins and thread)
• Map coloring: mandala, alternative mandalas, maps to color
• Erdos number, Jordan number and the Kevin Bacon game
• Tool for creating graphs and finding shortest paths

3. Platonic solids: Plato and the universe

• Tessellation construction: triangle, square, hexagon
• 17 ways to build planar mosaics
• Timaeus of Locri - Plato
• Construction of the Platonic solids
• Platonic solids and soap bubbles
• Archimedean solids
• Kaleidocycle
• Dodecahedral calendar (PDF)
• Models of the Kepler-Poinsot solids: Great stellated dodecahedron, Small stellated dodecahedron, Great icosahedron, Great dodecahedron, Star lamp
• Construction of a hypercube (PDF)

4. Derivatives: the mathematics of change

• The tangent line - Direction of the train
• Calculators: WolframAlpha, Symbolab
• Optimization - The cinema popcorn box

5. Mathematical models: pandemics and COVID-19

• Newton’s law of cooling
• The professor’s murder
• Lotka-Volterra predator-prey model
• Epidemic board game: board (PDF), online simulation
• Analytical solution of the SIR model (section 4.3)
• SIR model simulation
• Poster of significant events in virology
• COVID-19 data portals