- Title Pages
- Praise for <i>How to Free Your Inner Mathematician</i>
- Dedication
- Acknowledgments
- Introduction
- 21 Search for like-minded math friends, because of the Twin Prime Conjecture
- 22 Abandon perfectionism, because of the Hairy Ball Theorem
- 23 Enjoy the pursuit, as Andrew Wiles did with Fermat’s Last Theorem
- 24 Design your own pattern, because of the Penrose Patterns
- 25 Keep it simple whenever possible, since 0.999…=1
- 26 Change your perspective, with Viviani’s Theorem
- 27 Explore, on a Mobius strip
- 28 Be contradictory, because of the infinitude of primes
- 29 Cooperate when possible, because of game theory
- 30 Consider the less traveled path, because of the Jordan Curve Theorem
- 31 Investigate, because of the golden rectangle
- 32 Be okay with small steps, as the harmonic series grows without bound
- 33 Work efficiently, like bacteriophages with icosahedral symmetry
- 34 Find balance, as in coding theory
- 35 Draw a picture, as in proofs without words
- 36 Incorporate nuance, because of fuzzy logic
- 37 Be grateful when a solution exists, because of Brouwer’s Fixed Point Theorem
- 38 Update your understanding, with Bayesian statistics
- 39 Keep an open mind, because imaginary numbers exist
- 40 Appreciate the process, by taking a random walk
- 41 Fail more often, just like Albert Einstein did with E=mc2
- Solutions
- Bibliography
- Index
Investigate, because of the golden rectangle
Investigate, because of the golden rectangle
- Chapter:
- (p.187) 31 Investigate, because of the golden rectangle
- Source:
- How to Free Your Inner Mathematician
- Author(s):
Susan D'Agostino
- Publisher:
- Oxford University Press
“Investigate, because of the golden rectangle” offers mathematics students and enthusiasts inspiration for mathematical play by way of a guided construction of the golden rectangle. The discussion is illustrated with numerous hand-drawn sketches. A golden rectangle is a rectangle whose side lengths are in the golden ratio, which is, where the Greek letter (pronounced “phi”) is approximately equal to. Readers learn that an indirect, even haphazard, approach in mathematical play may lead to unanticipated discoveries. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.
Keywords: investigate, golden rectangle, math, student, golden ratio, discovery
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- Title Pages
- Praise for <i>How to Free Your Inner Mathematician</i>
- Dedication
- Acknowledgments
- Introduction
- 21 Search for like-minded math friends, because of the Twin Prime Conjecture
- 22 Abandon perfectionism, because of the Hairy Ball Theorem
- 23 Enjoy the pursuit, as Andrew Wiles did with Fermat’s Last Theorem
- 24 Design your own pattern, because of the Penrose Patterns
- 25 Keep it simple whenever possible, since 0.999…=1
- 26 Change your perspective, with Viviani’s Theorem
- 27 Explore, on a Mobius strip
- 28 Be contradictory, because of the infinitude of primes
- 29 Cooperate when possible, because of game theory
- 30 Consider the less traveled path, because of the Jordan Curve Theorem
- 31 Investigate, because of the golden rectangle
- 32 Be okay with small steps, as the harmonic series grows without bound
- 33 Work efficiently, like bacteriophages with icosahedral symmetry
- 34 Find balance, as in coding theory
- 35 Draw a picture, as in proofs without words
- 36 Incorporate nuance, because of fuzzy logic
- 37 Be grateful when a solution exists, because of Brouwer’s Fixed Point Theorem
- 38 Update your understanding, with Bayesian statistics
- 39 Keep an open mind, because imaginary numbers exist
- 40 Appreciate the process, by taking a random walk
- 41 Fail more often, just like Albert Einstein did with E=mc2
- Solutions
- Bibliography
- Index
