Pythagoras' theorem: the sacred geometry of triangles
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
RBA
2012
|
| Schriftenreihe: | Everything is mathematical
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | 151 S. Ill., graph. Darst., Kt. |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804149634491219968 |
|---|---|
| adam_text | Contents
Preface
.................................................................................................................................................
и
Chapter
1.
Pythagoras and the dawn of mathematics
13
The first civilisations
.................................................................................................................... 14
Building the Great Pyramid
............................................................................................ 17
Greek scientific thought
........................................................................................................... 20
Pythagoras and the Pythagoreans
......................................................................................... 22
The Golden Verses
................................................................................................................. 25
Philosophy and the science of the Pythagoreans
....................................................... 26
Mathematical harmony
........................................................................................................ 27
The divine number
.............................................................................................................. 29
The legacy of Pythagoreanism
....................................................................................... 34
Chapter
2.
History s most celebrated theorem
39
Good morning, numbers!
......................................................................................................... 39
Pythagoras theorem: formulation and history
............................................................ 41
Beautiful proofs
............................................................................................................................... 45
Pythagoras theorem and
Chou
Peí
Suan Ching
.................................................. 45
Pythagoras theorem through the eyes of Euclid
.............................................. 47
Pythagoras theorem in Arabian mosaic
................................................................... 47
Pythagoras theorem in the eyes of Henry
Perigai
........................................... 48
Pythagoras theorem as proved by Leonardo da Vinci
.................................... 49
Other proofs and puzzles
................................................................................................... 49
A note on Pythagoras theorem and parallel lines
............................................. 52
Current use of Pythagoras theorem
.................................................................................. 54
Mathematical and scientific applications
................................................................. 54
Everyday applications: Pythagoras theorem and moving furniture
61
Chapter
3.
An invitation to explore
^2 ............................................................. 63
The history of
л/Г
(from
1800 b.c.
to the current day)
..........................................64
Fractional approximations of 2
...................................................................................66
Records in the calculation ofV2
..................................................................................68
The surprising irrationality ofv2
........................................................................................69
CONTENTS
The first proof of the irrationality of V2
..................................................................... 72
Further proofs of irrationality
............................................................................................... 72
A geometric proof
............................................................................................................... 73
A proof with factors
........................................................................................................... 73
A proof with calculus
(Miidós Lasckovich)
........................................................ 74
An ingenious graphical proof (Alexander J.
Hahn) ....................................... 74
A diagrammatic proof (Tom
Apostol)
.................................................................... 75
Geometric sketches of
v
2................................................................................................................ 76
DIN paper and photocopy formats
........................................................................................... 78
ƒ
numbers in photography
............................................................................................................... 82
л/І
in Gaudi s
Parque
Guell
...................................................................... ...................................... 83
Chapter
4.
Journey to the spiral of Theodoras
.......................................................... 85
Dynamic proportions of
vi ........................................................................................................ 87
Beauty and the golden ratio
........................................................................................................... 90
Polygons, polyhedra and roots
...................................................................................................... 92
V3 in the equilateral triangle and regular hexagon
.............................................. 92
v
2
in the square and the regular octagon
................................................................... 93
л/5
in the construction of regular pentagons
............................................................ 94
Pythagorean cosmogony with polyhedra
..................................................................... 96
Square roots, art and design
............................................................................................................ 97
Chapter
5.
Surprising uses of Pythagoras theorem
............................................... 103
Squaring shapes
...................................................................................................................................... 103
The sum of similar shapes
................................................................................................................ 107
The
lunes
of Hippocrates
................................................................................................................. 108
Leonardo da Vinci and the
lunes
............................................................................................... 110
Inequalities with Pythagoras
.......................................................................................................... 112
Inequality between
¡a-¥b
and
[а+ф
....................................................................... 112
Inequalities between arithmetic means and the geometric mean
................. 113
Inequalities between the hypotenuse and catheti
..................................................... 114
Pythagoras theorem and perspective
....................................................................................... 115
From where do I view a painting?
............................................................................................. 118
Van
der
Laans plastic number
....................................................................................................... 122
CONTENTS
Chapter
6.
Beyond the theorem of Pythagoras
......................................................... 125
From Pythagoras to
Fermat
and on to Wiles
................................................................... 125
Pythagorean ratios in other polygons
...................................................................................... 129
Completing the Pythagorean figure
................................................................................ 129
The cosine theorem
.................................................................................................................. 130
The parallelogram law
............................................................................................................ 131
Pythagoras in
3D ................................................................................................................................... 133
Practical measures without Pythagoras
......................................................................... 133
From the right-angled triangle to the straight tetrahedron
............................. 134
Pythagoras theorem and the spiral staircase
............................................................... 136
The Agnesi curve
......................................................................................................................... 139
Finally, imaginary numbers
........................................................................................................... 140
The omnipresent theory
................................................................................................................ 142
Pythagoras theorem on other surfaces
......................................................................... 142
Pythagoras theorem on other structures
..................................................................... 143
Epilogue
................................................................................................................................................... 145
Bibliography
....................................................................................................................................... 147
Index
............................................................................................................................................................. 149
Pythagoras Theorem
The sacred geometry of triangles
The relationship between the hypotenuse and the adjacent
sides of a right-angled triangle is one of the most important
scientific discoveries in the history of humanity. The
relationship has some surprising effects both in geometry
and in the theory of number. The theorem that describes this
relationship takes its name from Pythagoras, one of the most
intriguing and mysterious figures in the history of science.
The first mathematical superstar was also the leader of a
mystical circle who regarded mathematics as a religion that
would explain everything in the Universe.
|
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| discipline | Mathematik |
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| spelling | Alsina, Claudi 1952- Verfasser (DE-588)143990934 aut Pythagoras' theorem the sacred geometry of triangles Claudi Alsina London RBA 2012 151 S. Ill., graph. Darst., Kt. txt rdacontent n rdamedia nc rdacarrier Everything is mathematical Pythagoreischer Lehrsatz (DE-588)4176546-1 gnd rswk-swf Pythagoreischer Lehrsatz (DE-588)4176546-1 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025388700&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025388700&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
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| title | Pythagoras' theorem the sacred geometry of triangles |
| title_auth | Pythagoras' theorem the sacred geometry of triangles |
| title_exact_search | Pythagoras' theorem the sacred geometry of triangles |
| title_full | Pythagoras' theorem the sacred geometry of triangles Claudi Alsina |
| title_fullStr | Pythagoras' theorem the sacred geometry of triangles Claudi Alsina |
| title_full_unstemmed | Pythagoras' theorem the sacred geometry of triangles Claudi Alsina |
| title_short | Pythagoras' theorem |
| title_sort | pythagoras theorem the sacred geometry of triangles |
| title_sub | the sacred geometry of triangles |
| topic | Pythagoreischer Lehrsatz (DE-588)4176546-1 gnd |
| topic_facet | Pythagoreischer Lehrsatz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025388700&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025388700&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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