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Figurate numbers
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Description
Rating
Title
Figurate
numbers
Creator
Deza, Elena.
Contributors
Deza, M., 1934
World Scientific (Firm)
DescriptionAbstract
Figurate
numbers
have a
rich
history
with
many
applications
. The
main
purpose
of this
book
is
to
provide
a
thorough
and
complete
presentation
of the
theory
of
figurate
numbers
,
giving
much
of their
properties
,
facts
and
theorems
with
full
proofs
. This
book
is
the
first
of this
topic
written
in
unified
systematic
way
.
It
also
contains
many
exercises
with
solutions
.
DescriptionTable Of Contents
1
.
Plane
figurate
numbers
.
1.1
.
Definitions
and
formulas
.
1.2
.
Main
properties
of
polygonal
numbers
.
1.3
.
Square
triangular
numbers
.
1.4
.
Other
highly
polygonal
numbers
.
1.5
.
Amount
of a
given
number
in
all
polygonal
numbers
.
1.6
.
Centered
polygonal
numbers
.
1.7
.
Other
plane
figurate
numbers
.
1.8
.
Generalized
plane
figurate
numbers

2
.
Space
figurate
numbers
.
2.1
.
Pyramidal
numbers
.
2.2
.
Cubic
numbers
.
2.3
.
Octahedral
numbers
.
2.4
.
Other
regular
polyhedral
numbers
.
2.5
.
Some
semiregular
and
star
polyhedral
numbers
.
2.6
.
Centered
space
figurate
numbers
.
2.7
.
Other
space
figurate
numbers
.
2.8
.
Generalized
space
figurate
numbers

3
.
Multidimensional
figurate
numbers
.
3.1
.
Pentatope
numbers
and their
multidimensional
analogues
.
3.2
.
Biquadratic
numbers
and their
multidimensional
analogues
.
3.3
.
Other
regular
polytope
numbers
.
3.4
.
Nexus
numbers
.
3.5
.
Pyramidal
numbers
of the
second
order
and their
multidimensional
analogues
.
3.6
.
Centered
multidimensional
figurate
numbers
.
3.7
.
Generalized
multidimensional
figurate
numbers

4
.
Areas
of
number
theory
including
figurate
numbers
.
4.1
.
Addition
and
multiplication
tables
.
4.2
.
Pascal's
triangle
and
binomial
theorem
.
4.3
.
Pythagorean
triples
and
other
Diophantine
equations
.
4.4
.
Perfect
numbers
.
4.5
.
Mersenne
and
Fermat
numbers
.
4.6
.
Fibonacci
and
Lucas
numbers
.
4.7
.
Palindromic
numbers
.
4.8
.
Other
special
numbers
.
4.9
.
Prime
numbers
.
4.10
.
Magic
constructions
.
4.11
.
Unrestricted
partitions
.
4.12
.
Waring's
problem

5
.
Fermat's
polygonal
number
theorem
.
5.1
.
History
of the
problem
.
5.2
.
Lagrange's
foursquare
theorem
.
5.3
.
Gauss's
threetriangularnumber
theorem
;
elementary
considerations
.
5.4
.
Proof
of the
Gauss's
threetriangularnumber
theorem
.
5.5
.
Sums
of
squares
and
Minkowski's
convex
body
theorem
.
5.6
.
Cauchy's
proof
of the
polygonal
number
theorem
.
5.7
.
Pepin's
proof
of the
polygonal
number
theorem
.
5.8
.
Other
results
related
to the
problem

6
.
Zoo
of
figuraterelated
numbers

7
.
Exercises
.
Publisher
World Scientific Pub. Co.
Subject
Numbers, Polygonal.
Number theory.
Identifier
9789814355490
(electronic
bk.)
;
9814355488
;
9789814355483
;
http://www.worldscientific.com/worldscibooks/10.1142/8188#t=toc
Language
eng
Type
Electronic books.
FormatExtent
xviii, 456 p. : ill. (some col.)
Date
c2012
.
OCLC number
874497725
CONTENTdm number
361
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