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首页数学奇思妙想:探索有趣的数学世界
"Math Mutation Classics" 是一本由 Erik Seligman 撰写的书籍,它集合了作者在 MathMutation.com 博客上发布的最有趣、最具挑战性和启发性的数学文章。这本书通过独特的方式探讨数学,分析日常生活中的观察,并用证明来得出意想不到的结论。涵盖了广泛的数学主题,适合各个年龄层次和能力水平的读者。Erik Seligman 的视角将数学应用于从政治家到河马等各种话题,旨在提供一个不同寻常的思考角度,激发读者更创新的思维方式。 本书的内容深入浅出,探索数学的奇特、趣味和奇异之处,旨在让读者了解到有时候2+2也可能等于5,轮子不一定是圆形的,甚至可以数学证明你的地下室里有一只河马。它还引导读者如何识别四维生物穿越厨房的迹象。这些看似离奇的问题背后,实际上展示了数学在解决现实问题时的灵活应用和无限可能性。 书中的讨论不仅限于传统的数学概念,还包括了对现实世界的数学解析,如通过数学方法去辨别和理解我们周围的世界。作者鼓励读者跳出常规思维,用数学的眼光看待日常生活,从而发现隐藏的模式和规律。这种跨学科的思考方式能帮助读者开阔视野,提高逻辑推理能力,同时也能让学习数学的过程变得更加有趣和引人入胜。 这本书适合对数学有浓厚兴趣的读者,无论你是初学者还是资深爱好者,都能从中找到乐趣和挑战。通过阅读 "Math Mutation Classics",你不仅可以提升数学技能,还能培养出一种独特的数学思维,学会用数学的语言去解读世界,让生活中的点滴都充满了数学的魅力。
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■ CONTENTS
xv
A Universe Made of Math .................................................................... 181
From Math Mutation podcast 105 ........................................................................181
Mathematical Immortality ................................................................... 182
From Math Mutation podcast 178 ........................................................................182
■Appendix: References and Further Reading ............................... 185
Chapter 1: Simple Surprises ................................................................ 185
City of Mutants .....................................................................................................185
Two Plus Two Equals Five .....................................................................................185
Stupid Number Tricks ...........................................................................................186
Deceptive Digits ....................................................................................................186
Nonrandom Randomness .....................................................................................186
A True Holiday Celebration ....................................................................................186
Forgotten Knowledge ...........................................................................................186
Exponents Squared ...............................................................................................186
Giving You The Fingers..........................................................................................187
Chapter 2: Into Infi nity ......................................................................... 187
Too Infi nite For Me ................................................................................................187
Infi nitely Ahead of His Time ..................................................................................187
Infi nite Infi nities ....................................................................................................187
Infi nity Times Infi nity ............................................................................................187
Infi nite Perimeter, Finite Area ...............................................................................188
A Pretty Big Library ...............................................................................................188
Someone Knocked My 8 Over ...............................................................................188
Not Quite Infi nity ...................................................................................................188
Big Numbers Upside Down ...................................................................................188
Chapter 3: Getting Geometric .............................................................. 189
Something Euclid Missed .....................................................................................189
How Not To Decorate Your Bathroom ....................................................................189
Bees Vs Mathematicians ......................................................................................189
www.it-ebooks.info
■ CONTENTS
xvi
A Brush With Evil ..................................................................................................189
Twistier Than You Thought ....................................................................................190
Squash Those Dice ...............................................................................................190
Crazy Dice .............................................................................................................190
Wheels That Aren’t Round ....................................................................................190
The Future That Never Arrived ..............................................................................191
Chapter 4: Deeper Dimensions ............................................................ 191
Making Flatland Real ............................................................................................191
Is Flatland Doomed? .............................................................................................191
Visitors From The Next Dimension ........................................................................191
Will The Real Fourth Dimension Please Stand Up? ...............................................191
A Four Dimensional House....................................................................................192
Turning Around In Time .........................................................................................192
11-Dimensional Spaghetti Monsters ....................................................................192
Your Five Dimensional Kitchen .............................................................................192
As Math Goes By ...................................................................................................192
Between The Dimensions .....................................................................................192
Chapter 5: Understanding The Universe .............................................. 193
The Bogus Bang? ..................................................................................................193
The Shape of the Universe ....................................................................................193
Your Size in Space and Time ................................................................................193
Observing the Universe ........................................................................................193
Alien Algebra.........................................................................................................193
Time Reversed Worlds ..........................................................................................193
A Pear Shaped Planet ...........................................................................................194
Where Am I? .........................................................................................................194
Putting the Multiverse to Work .............................................................................194
www.it-ebooks.info
■ CONTENTS
xvii
Chapter 6: The Mathematical Mind ..................................................... 195
What Color Is This Podcast? .................................................................................195
Computers On The Brain .......................................................................................195
The Rain Man’s Secret ..........................................................................................195
Look Him In The Eye .............................................................................................195
Savants Are People Too.........................................................................................195
The Uninhibited Brain ...........................................................................................195
A Logical Language ..............................................................................................196
When ‘Is’ Isn’t .......................................................................................................196
De-Abstracting Your Life .......................................................................................196
Your Kids Are Smarter Than You ...........................................................................196
My Brain Hurts ......................................................................................................197
Psychochronometry ..............................................................................................197
Chapter 7: Science and Skepticism ..................................................... 197
Why Statisticians Stink at Statistics .....................................................................197
On Average, Things Are Average ...........................................................................197
Don’t Panic ...........................................................................................................197
It Must Be True, There’s An Equation ....................................................................198
A Twisted Take on Turing ......................................................................................198
I Want My Molecule ..............................................................................................198
The Gullible Ratio ..................................................................................................198
Monkeying Around With Probability ......................................................................198
Solving Burma’s Problems ....................................................................................199
A New Numerology ...............................................................................................199
One Intestinal Worm Per Child ..............................................................................199
Chapter 8: Analyzing The Arts .............................................................. 199
Discovering the Third Dimension ..........................................................................199
A New Perspective on Perspective .......................................................................199
Hippasus’s Revenge .............................................................................................200
www.it-ebooks.info
■ CONTENTS
xviii
Unlistenable But Fun ............................................................................................200
What a Planet Sounds Like ...................................................................................200
Mozart Rolls the Dice ............................................................................................200
Candide’s Calculus ...............................................................................................200
Fractals in the Hat ................................................................................................201
Math or Not Math? ................................................................................................201
Gnarly Gnovels ......................................................................................................201
Chapter 9: Political Ponderings ........................................................... 201
A Founding Theorem .............................................................................................201
More Than a Cartoon Cat ......................................................................................201
The Round Road to Damnation .............................................................................201
A Math Teacher to Remember ..............................................................................202
Election Solutions .................................................................................................202
Democracy Doesn’t Work......................................................................................202
Drop That Number or We’ll Shoot .........................................................................202
That’s How We Do It In Government .....................................................................202
Chapter 10: Money Matters ................................................................. 202
Tally Folly ..............................................................................................................202
How to Bankrupt Your Boss and Get Rich .............................................................203
What Color Is Your Swan? .....................................................................................203
Comparative Disadvantage ...................................................................................203
Money for Math ....................................................................................................203
Liking the Lottery ..................................................................................................203
Number Nonsense ................................................................................................204
Does The House Always Win? ...............................................................................204
Mutating Up the Corporate Ladder .......................................................................204
The Converse of a CEO .........................................................................................204
www.it-ebooks.info
■ CONTENTS
xix
Chapter 11: Looking at Life ................................................................. 204
Florence Nightingale, Math Geek ..........................................................................204
The Genius Who Cheated ......................................................................................205
Shuttle Butt ...........................................................................................................205
Booms and Busts ..................................................................................................205
The Boids and Bees of Leadership .......................................................................205
A New Kind of Decade ..........................................................................................205
Basic Bugs ............................................................................................................206
Bugged By Math ...................................................................................................206
Voyages Through Animalspace .............................................................................206
A Heap of Seagulls ...............................................................................................206
Chapter 12: Puzzling Paradoxes .......................................................... 206
You Can Cross the Road ........................................................................................206
Four Dimensional Greek Warships ........................................................................206
A Christmas Surprise ............................................................................................207
Resolving the Grandfather Paradox ......................................................................207
A Million Dollar Choice ..........................................................................................207
The Painter’s Paradox ...........................................................................................207
The Monty Haul Paradox .......................................................................................207
A Mathematical Nuclear Bomb .............................................................................207
Chapter 13: Rethinking Reality ............................................................ 208
Answering All Possible Questions .........................................................................208
Sacrifi cing a Goat to Calculus ...............................................................................208
Grue and Bleen .....................................................................................................208
Hippos in My Basement ........................................................................................208
Is There a Hippopotamus In This Podcast? ...........................................................208
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