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Friberg J. — Unexpected Links Between Egyptian And Babylonian Mathematics
Friberg J. — Unexpected Links Between Egyptian And Babylonian Mathematics

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Название: Unexpected Links Between Egyptian And Babylonian Mathematics

Автор: Friberg J.

Аннотация:

Mesopotamian mathematics is known from a great number of cuneiform texts, most of them Old Babylonian, some Late Babylonian or pre-Old-Babylonian, and has been intensively studied during the last couple of decades. In contrast to this Egyptian mathematics is known from only a small number of papyrus texts, and the few books and papers that have been written about Egyptian mathematical papyri have mostly reiterated the same old presentations and interpretations of the texts.

In this book, it is shown that the methods developed by the author for the close study of mathematical cuneiform texts can also be successfully applied to all kinds of Egyptian mathematical texts, hieratic, demotic, or Greek-Egyptian. At the same time, comparisons of a large number of individual Egyptian mathematical exercises with Babylonian parallels yield many new insights into the nature of Egyptian mathematics and show that Egyptian and Babylonian mathematics display greater similarities than expected.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 294

Добавлена в каталог: 19.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\overline{10}\cdot n$ table      29 32 211
$\overline{90}$ and $\overline{150}$ tables      165 211
'Since he said'      206
'Since it was said to you'      206
2/n table      29 96 144 150
Algorithm, doubling and halving      18
Algorithm, trailing part      8
Almost round area numbers      51 52 53 56 114
Basket, area of semicircle      78
Bread rations of various sizes      63 66
Buying and selling exercise      217 218
Circle area rule, Babylonian      42
Circle area rule, demotic      123 127 131 142
Circle area rule, Greek      195 198
Circle area rule, hieratic      40 42 44 85 98
Circle constants      42
Circle segment (corrupt text)      133
Circle segment area rule      see "Segment area rule"
Circle segments, constants      134
Circle, given area, unknown diameter      122
Circle-and-chord problem      138 139 141
Circles and a segment of a circular band      196
Circular bands, concentric      197
Combined baking number      60
Combined market rate      60 103 207 214
Combined work norm      69 70
Completing the square      208
Completion problem      27 29 96 106 112
Cone ("log")      142 143 211
Cone (mast)      142
Cone (storeroom)      211
Cone (water clock)      195
Cone, truncated      234 242 262
Corrupt text      30 37 44 133 153
Cylindrical vessels, content      86 88 206
Division problem, applied      25 35 36
Division problem, repeated      30 32 33 102 204
Division problems      28 30 109
Doubling and halving algorithm      18 22
Drawing of basket (semicircle?)      79
Drawing of birectangle      230
Drawing of circle      42 85 98
Drawing of circle and square      41
Drawing of circles, etc.      197
Drawing of equilateral triangle in circle      128 130
Drawing of pyramid and cone      58
Drawing of rectangles and trapezoid      167
Drawing of rectangular field      157
Drawing of rectangular field, schematic      158
Drawing of rectangular granary      44
Drawing of square in circle      131 135
Drawing of striped trapezoids      175ff
Drawing of striped triangle      45ff 49
Drawing of trapezoid      52 72
Drawing of trapezoids, nonsymmetric      221ff
Drawing of triangle in circle      139
Drawing of triangular pyramids      234
Drawing of truncated pyramid      76
Drawing of upright triangles      238
Elements I, 39, 41      193
Elements I, Definitions      193
Elements I, essay on      193
Elements II, exercises      193
Elements XIII, 10, 16      193
Equilateral triangle in a circle      126 129
Equilateral triangle, area      127 129 156 237 238
Equilateral triangular base of pyramid      235
Equipartitioned trapezoid      181 188
Fractions, counting with      150ff
Fractions, operations with      212ff
Granary, cylindrical      85
Granary, rectangular      211
Granary, repeated division problem      33
Granary, square and circular      44
Height of unsymmetric triangle      224
Icosahedron, outer shell      236
Iterated sum of 10 first integers      145
Land survey, eight fields      194
Land survey, four fields      159 194
Land survey, one field      162
Linear equations      174
Linear equations, four metals      67 168
Linear equations, iron and gold      67 170
Linear equations, system of      68 170
Linear equations, systems of      173 200ff
Many-digit decimal numbers      90
Metric algebra, area and diagonal      125 126
Metric algebra, area and side ratio      73 115
Metric algebra, diagonal and side ratio      81
Metric algebra, expanded rectangle      57
Metric algebra, quadrilateral      160
Metric algebra, rectangle      136 221
Metric algebra, reshaping a rectangle      110 115 120
Metric algebra, striped triangle      45f 54
Metric algebra, trapezoid      72 115
Metric algebra, triangle      71
Multiplication algorithm, explicit      149
Multiplication rule      149
Multiplication table, times 64      149
Non-symmetric trapezoids      221
Non-symmetric trapezoids, birectangle      40 226
Orientation of circular segment      128
Original length of a reed      117 144 208
Outline of text      61 95 98 100 101 249
Plimpton 322      82 93 155
Pole against a wall      107 108
Powers of 2, 64      23
Prices and market rates      61 68 214 215
Progression, 10 brothers      37
Progression, 10 terms      89
Progression, 30 terms      14 21
Progression, 4 brothers      122
Progression, 4 terms (tgs?)      121
Progression, 5 brothers      38
Progression, arithmetic, 5 persons      39
Progression, geometric, sum of      2 11 12
Progression, quasi-arithmetic, 5 brothers      38
Progression, sum of, 7 brothers      9
Pyramid and cone? seked      58
Pyramids and cones      76 233ff 249
Quadratic-linear system of equations      81 83 84 206
Quadrilateral area rule      157 159 160 165
Quadrilateral area rule, general      161
Quadrilateral, schematic      158 194
Quasi-cube table      148
Reciprocal of 1 + 1/n      143
Reciprocal of 1 - 1/5      117
Reciprocal of 1 - 1/6      117
Reshaping a rectangle      120
Reshaping a rectangular cloth      115
Ridge pyramid, volume of      77 245
Right triangles, problems      220
Segment area rule      129ff 133 139 199
Semi-regular square sides      156
Semicircle (basket), area of      78
Semicircle, constants      80 81
Semicircle, problem for a      80
Series of exercises      251
Sharing problems      29
Square in a circle      131 135
Square side rule      155
Striped trapezoids      174ff 188
Striped triangle      45 48 49 98 102 181
Sum of 10 first square numbers      10
Symmetric trapezoid      225
Table Of Contents      27 69 106 208 234
Table of contents and outline of the text      61 95 98 249
Table of powers      6
Table of powers, descending      7
Tables for reed measure      163
Tables of fractions      210
Tabular array, combined market rate      207
Tabular array, combined work norm      70
Tabular array, cost of excavation      206
Tabular array, quadratic-linear equations      84
Tabular array, sheep and lambs      207
Tabular array, systems of linear equations      200ff
Tabular array, unequal shares      207
Thousand-cubit-strip      40 158
Trailing part algorithm      8
Trapezoid with vertical transversals      182ff
Truncated cone      234 264
Truncated pyramid, square      74 234 243
Truncated pyramid, triangular      234
Truncated pyramid, with ridge      252
Unequal sharing, gold, silver, lead      67
Unequal sharing, loaves      36ff
Work norm, volume of a ring wall      186
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