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Blink 3 of 8 - The 5 AM Club
by Robin Sharma
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In Pursuit of the Unknown summary
Ian Stewart
17 Equations That Changed the World
22 mins
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Table of Contents
In Pursuit of the Unknown
Summary of 9 key ideas
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The Pythagorean theorem shaped our understanding of geography and Earth’s place in the solar system.
On the surface, the Pythagorean theorem looks simple. Made up of the equation a²+b²=c², it explains the relationship between the three sides of a right-angled triangle where a and b represent the sides that form the right angle and c is the longest side.
Despite its simplicity, the theorem was a vital first step in developing the geometric techniques needed for making accurate maps: triangulation. Since all polygons can be cut into triangles, and all triangles can be cut into two right-angled triangles, the equation allows us to calculate the sides and angles of any polygon. In mapmaking, the area being surveyed is covered with a network of triangles, which allows us to measure distances and angles between stretches of land.
Because of technological advancements in measuring tools, explicit triangulation is no longer used. However, it’s still there in the methods used to deduce locations from the satellite data.
Generalizations of Pythagoras’s theorem also enable us to measure the shape of the universe. The Earth has the shape of a sphere, sure, but what about the universe? Finding the answer to this question seems like an impossible task: after all, we can’t step outside to see what shape it is.
However, thanks to generalizations of Pythagoras’s theorem, there is something else we can do.
Pythagoras’s theorem applies to triangles in a flat plane. But generalizations of it can apply to triangles in spaces that are curved. For example, applying triangles onto a sphere makes it possible to measure our planet. But there’s more: these generalizations can also tell us how curved the spaces are. So by measuring triangles within space, we can try to compute its curvature.
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What is In Pursuit of the Unknown about?
In this book, Ian Stewart focuses on 17 famous equations in mathematics and physics history, highlighting their impact on society. Stewart gives a brief history of the wonders of scientific discovery, and peppers it with vivid examples and anecdotes.
Best quote from In Pursuit of the Unknown
Equations are the lifeblood of mathematics, physics and technology. Without them, our world would not exist in its present form.
—Ian Stewart
Who should read In Pursuit of the Unknown?
- Anyone interested in how mathematical ideas affect science and society
- Anyone who’s always been scared of complicated-looking formulas
- Anyone fascinated by the beauty and hidden power of formulas
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