2⁵ Problems for STEM Education

397 Pages·2020·76.565 MB·English

by  Valery Ochkov

25 Problems for STEM Education

25 Problems for STEM Education
Valery F. Ochkov
Moscow Power Engineering Institute
CRC Press
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Contents
Acknowledgment,xiii
Author,xv
INTRODUCTION, XVII
STUDY 1 ◾ Formulas for Calculations Or: Chekhov’s Gun 1
ABSTRACT 1
REFERENCES 8
STUDY 2 ◾ Swan, Crayfsh and Pike Or: Scalar and Vector in Computer Calculations 9
ABSTRACT 9
REMARK 10
AFTERWORD 13
CONCLUSIONS 16
STUDY 3 ◾ The Gold-Bug Or: Roman-Arab Cryptography 17
ABSTRACT 17
ASSIGNMENTS FOR READERS 24
STUDY 4 ◾ Solvers Or: The Mathcad Magnifcent Seven 25
ABSTRACT 25
INTRODUCTION 25
PROBLEM 1 26
Solve 26
root+root 27
Polyroots 31
Find 31
PROBLEM 2 31
lsolve 33
Minimize and Maximize 33
PROBLEM 3 33
Minerr 34
CONCLUSIONS 35
ASSIGNMENTS FOR READERS 35
vii
viii ◾ C ontents
STUDY 5 ◾ Guess the Image Or: The Matrix Game 37
ABSTRACT 37
GUESSING NOT THE IMAGE BUT MELODY 40
ASSIGNMENTS FOR READERS 41
STUDY 6 ◾ How Much Or: The Old Problem in a New Way 43
ABSTRACT 43
PROBLEM 1 47
PROBLEM 2 49
PROBLEM 3 51
REFERENCE 52
STUDY 7 ◾ Catenary Or: The Fifth Element 53
ABSTRACT 53
SQUARE WHEEL 67
CONTINUING STUDY 7 67
Also about a Chain (Circles), but Electrical 68
ELECTRICAL COMMENTARY 71
AND THE LAST 75
ASSIGNMENTS FOR READERS 78
STUDY 8 ◾ Live Kinematic Schemes Or: Arm of Hella 81
ABSTRACT 81
THE ARM OF HELLA 89
JOURNEY INTO THE WORLD OF SCIENCE AND ART ON THE PLANTIGRADE MACHINE 90
LET’S MOVE AHEAD 95
AND FINALLY 96
ASSIGNMENTS FOR READERS 98
STUDY 9 ◾ Celestial Mechanics Or: Kepler’s Watch 99
ABSTRACT 99
LAWLESS COMET 109
And Last but One for the Most Curious and Meticulous 114
ASSIGNMENTS FOR READERS 119
STUDY 10 ◾ Recursion Or: A Knight’s Tour 121
ABSTRACT 121
STUDY 11 ◾ Yes–No in Mathcad Or: Boole’s Origami 127
ABSTRACT 127
BOOLEAN FUNCTIONS OF ONE ARGUMENT 127
Contents    ◾    ix
BOOLEAN FUNCTIONS OF TWO ARGUMENTS 128
FUNCTIONS OF MANY ARGUMENTS 137
A SAD NOTE 137
ASSIGNMENTS FOR READERS 138
STUDY 12 ◾ Fuzzy Sets Or: Optimal Fire Bucket 139
ABSTRACT 139
PROBLEM 1 141
PROBLEM 2 143
And at Last 150
ASSIGNMENTS FOR READERS 150
STUDY 13 ◾ The Journey of a Circle in a Triangle, and of a Triangle in a Hollow Or: A Self-
Directed Computer Director 151
ABSTRACT 151
ASSIGNMENTS FOR READERS 160
STUDY 14 ◾ Interpolation, Extrapolation and Fitting Or: Lies, Damned Lies and Statistics 161
ABSTRACT 161
ASSIGNMENTS FOR READERS 178
STUDY 15 ◾ Go There, Knowing Where to Go Or: New Swiss Watches 179
ABSTRACT 179
LET’S START WITH THE CLOCK 179
PROBLEM 1 187
PROBLEM 2 187
PROBLEM 3 188
ASSIGNMENTS FOR READERS 191
STUDY 16 ◾ Heads or Tails Or: A Three-Way Duel in Monte Carlo 193
ABSTRACT 193
ASSIGNMENTS FOR READERS 199
STUDY 17 ◾ Geese Are Flying Or: The Problem of Fishermen and Fish 201
ABSTRACT 201
ASSIGNMENTS FOR READERS 204
STUDY 18 ◾ Alphabetical Puzzle Or: Help Yourself So That the Computer Helps You! 205
ABSTRACT 205
ASSIGNMENTS FOR READERS 208