Roots to Research: A Vertical Development of Mathematical Problems

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American Mathematical Soc., Jan 1, 2007 - Mathematics - 338 pages
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Certain contemporary mathematical problems are of particular interest to teachers and students because their origin lies in mathematics covered in the elementary school curriculum and their development can be traced through high school, college, and university level mathematics. This book is intended to provide a source for the mathematics (from beginning to advanced) needed to understand the emergence and evolution of five of these problems: The Four Numbers Problem, Rational Right Triangles, Lattice Point Geometry, Rational Approximation, and Dissection. Each chapter begins with the elementary geometry and number theory at the source of the problem, and proceeds (with the exception of the first problem) to a discussion of important results in current research. The introduction to each chapter summarizes the contents of its various sections, as well as the background required. The book is intended for students and teachers of mathematics from high school through graduate school. It should also be of interest to working mathematicians who are curious about mathematical results in fields other than their own. It can be used by teachers at all of the above mentioned levels for the enhancement of standard curriculum materials or extra-curricular projects. -- Book cover.
 

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Contents

I
1
II
2
III
5
IV
11
V
15
VI
17
VII
22
VIII
26
XXXVIII
193
XXXIX
195
XL
197
XLI
201
XLII
204
XLIII
205
XLIV
208
XLV
210

IX
32
X
41
XI
45
XII
47
XIII
48
XIV
63
XV
69
XVI
84
XVII
90
XVIII
94
XIX
96
XX
101
XXI
104
XXII
109
XXIII
112
XXIV
121
XXV
123
XXVI
126
XXVII
130
XXVIII
137
XXIX
145
XXX
157
XXXI
162
XXXII
166
XXXIII
169
XXXIV
172
XXXV
176
XXXVI
183
XXXVII
185
XLVI
215
XLVII
221
XLVIII
230
XLIX
232
L
233
LI
236
LII
241
LIII
243
LIV
245
LV
251
LVI
257
LVII
259
LVIII
266
LIX
269
LX
277
LXI
280
LXII
283
LXIII
290
LXIV
295
LXV
297
LXVI
298
LXVII
311
LXVIII
315
LXIX
323
LXX
325
LXXI
333
LXXII
335
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