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The Beauty of Everyday Mathematics / by Norbert Herrmann
Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerLink BücherPublisher: Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2012Description: Online-Ressource (XIII, 138p. 35 illus, digital)ISBN:- 9783642221040
- 510
- QA1-939
- QA43 .H47 2012
Contents:
Summary: Preface -- The Soda Can Problem -- The Mirror Problem -- The Leg Problem -- The Sketch Problem -- the Parallel Parking Problem -- The Parking Garage Problem -- the 85th Birthday Problem -- The Slippery-Ice of Bread-Slicing Problem -- the Snail-Racehorse Problem -- The Discus Thrower Problem -- The Beer Coaster Problem -- the Toasting Problem -- The Heart Problem -- Index.Summary: Imagine that you’ve finally found a parking space after a long and harrowing search, but are now encountering some difficulty in trying to enter this space. Wouldn’t it be great if you knew a formula that allowed you to enter the space without difficulty? Are you annoyed because your soda can doesn’t remain upright during a picnic? Would you like to know why a mirror swaps right and left, but not top and bottom? Are you looking for a mathematical speech to toast your mother-in-law’s 85th birthday? Or do you want to give your heart away mathematically? Dr. Norbert Herrmann provides amusing and entertaining solutions to these and many other problems that we encounter in everyday situations. “A book for teachers, students of mathematics, and anybody who likes unusual and amusing calculations.” .PPN: PPN: 165108758XPackage identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
The Beauty of Everyday Mathematics; Preface; Contents; Chapter 1 The Soda Can Problem; 1.1 Introduction; 1.2 The Problem; 1.3 Determining the Center of Gravity; 1.4 The Lowest Position of the Center of Gravity; Determination by Thought Experiment; Determination Through Analytical Considerations; 1.5 Drinking in Two Mouthfuls; 1.6 Center of Gravity of an Ordinary Can; 1.7 Final Remarks; Chapter 2 The Mirror Problem; 2.1 Introduction; 2.2 The Mirror Problem for Individuals; 2.3 The Mirror Problem for Groups; 2.4 The Problem; 2.5 The Mirror Problem Expressed Mathematically
2.6 Results of Analysis of the Mirror ProblemChapter 3 The Leg Problem; 3.1 Introduction; 3.2 The Problem; 3.3 The Physical Model; 3.4 Analytical Solution; 3.5 Graphical Solution; 3.6 Application and Comments; 3.7 A Mnemonic Device for p; 3.8 Comments on the Number p; Chapter 4 The Sketch Problem; 4.1 Introduction; 4.2 The Problem; The Sketch Problem; 4.3 The "Proof"; 4.4 The First Clue; 4.5 The Complete Truth; 4.6 The Moral; Chapter 5 The Parallel Parking Problem; 5.1 Introduction; 5.2 The Problem; 5.3 Rebecca Hoyle's Formula; 5.4 Criticizing Hoyle's Formula; 5.5 The Turning Circle
5.6 The Center of the Turning Circle5.7 The Smallest Possible Circle; 5.8 The Effective Radius; 5.9 Our Model Car; 5.10 New Formulas for Parallel Parking; 5.11 The Formula for a 45 degree Maneuver; 5.12 The Optimal Formulas; 5.13 Conclusions; The new formulas for parking; 5.14 Values for a Few Cars; 5.15 A Little Mental Exercise; Chapter 6 The Parking Garage Problem; 6.1 Introduction; 6.2 The Problem; 6.3 Forward Parking; 6.4 Backward Parking; Chapter 7 The 85th Birthday Problem; 7.1 Dear Mother-in-Law; 7.2 What Do Mathematicians Do?; 7.3 The Numbers of Your Life; 7.4 The Number Zero
The Definition of ZeroThe Uniqueness of Zero; Multiplying by Zero Gives Us Nothing; Division by Zero; Hilbert's Hotel; 7.5 The Number 85; Card Game; 7.6 85 Is Everywhere; 7.7 State Capital Problem; Chapter 8 The Slippery-Ice or Bread-Slicing Problem; 8.1 Introduction; 8.2 The Problem; 8.3 Physical Background; 8.4 The Mathematical Model; 8.5 The Solution; Laplace Transformation; 8.6 The Result; 8.7 Interpretation of the Result; 8.8 Some Further Remarks; 8.9 A Little Brain Teaser; Chapter 9 The Snail-Racehorse Problem; 9.1 Introduction; 9.2 The Problem; 9.3 Mathematical Formulation
9.4 Solution of the Differential Equation9.5 Calculating the Time of Meeting; 9.6 Evaluating the Example; 9.7 Solution of State Capital Problem; Chapter 10 The Discus Thrower Problem; 10.1 Introduction; 10.2 The Problem; 10.3 The "Loss" Formula; Graphic(al) Derivation; Mathematical Derivation; 10.4 Application; Chapter 11 The Beer Coaster Problem; 11.1 Introduction; 11.2 The Problem; 11.3 Physical Background; 11.4 Mathematical Description; 11.5 The Solution; The Fixed-point Procedure; Fixed-point Procedure; The Newton Procedure; Newton Procedure; 11.6 Application to the Beer Coaster Problem
Solution by the Fixed-point Procedure
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