figurate numbers

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Figurate Numbers

Author : Elena Deza
ISBN : 9789814355483
Genre : Mathematics
File Size : 52. 26 MB
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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.

Figurate Numbers

Author : Books, LLC
ISBN : 1155824636
Genre : Crafts & Hobbies
File Size : 77. 24 MB
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 22. Chapters: Polygonal number, Polite number, Square number, Centered square number, Triangular number, Figurate number, Cube, Centered polygonal number, Square triangular number, Pentagonal number, Octahedral number, Square pyramidal number, Centered hexagonal number, Fermat polygonal number theorem, Pronic number, Tetrahedral number, Star number, Heptagonal number, Centered triangular number, Pentatope number, Gnomon, Centered nonagonal number, Centered decagonal number, Pentagonal pyramidal number, Centered heptagonal number, Centered octagonal number, Dodecagonal number, Pollock octahedral numbers conjecture, Centered pentagonal number, Centered cube number, Hectagonal number, Heptagonal pyramidal number, Hexagonal pyramidal number, Myriagonal number. Excerpt: In mathematics, a polygonal number is a number represented as dots or pebbles arranged in the shape of a regular polygon. The dots were thought of as alphas (units). These are one type of 2-dimensional figurate numbers. The number 10, for example, can be arranged as a triangle (see triangular number): But 10 cannot be arranged as a square. The number 9, on the other hand, can be (see square number): Some numbers, like 36, can be arranged both as a square and as a triangle (see square triangular number): By convention, 1 is the first polygonal number for any number of sides. The rule for enlarging the polygon to the next size is to extend two adjacent arms by one point and to then add the required extra sides between those points. In the following diagrams, each extra layer is shown as in red. Triangular numbers Square numbers Polygons with higher numbers of sides, such as pentagons and hexagons, can also be constructed according to this rule, although the dots will no longer form a perfectly regular lattice like above. Pentagonal numbers Hexagonal numbers If s is the n...

Figurate Numbers

Author : Edmund A.. Engler
ISBN : OCLC:9138718
Genre : Number theory
File Size : 44. 71 MB
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Mathematics Polygons

Author : Source Wikia
ISBN : 1234827212
Genre :
File Size : 90. 54 MB
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This book consists of articles from Wikia. Pages: 44. Chapters: Figurate numbers, Quadrilaterals, Triangles, Centered polygonal number, Figurate number, Pentatopic number, Polygonal number, Pyramidal number, Square pyramidal number, Tetrahedral number, Trapezoidal number, Triangular number, Decagon, Digon, Dodecagon, Golygon, Henagon, Hendecagon, Heptagon, Hexagon, Nonagon, Octagon, Pentagon, Perimeter, Polygon, Right triangle, Triangle, Brahmagupta's formula, Bretschneider's formula, Isosceles trapezoid, Kite, Rectangle, Rhombus, Square, Trapezoid, Trapezoidal number, Circumscribed circle, Equilateral triangle, Heronian triangle, Isosceles triangle, Mollweide's formula, Right triangle, Scalene triangle, Special right triangles, Triangle, Triangular number, Trigonometry. Excerpt: The centered polygonal numbers are a class of series of figurate numbers, each formed by a central dot, surrounded by polygonal layers with a constant number of sides. Each side of a polygonal layer contains one dot more than a side in the previous layer, so starting from the second polygonal layer each layer of a centered k-gonal number contains k more points than the previous layer. These series consist of the and so on. The following diagrams show a few examples of centered polygonal numbers and their geometric construction. (Compare these diagrams with the diagrams in Polygonal number.) Centered square numbers Centered hexagonal numbers As can be seen in the above diagrams, the nth centered k-gonal number can be obtained by placing k copies of the (n

Figurate Numbers In The Mathematical Tradition Of Al Andalus And The Maghrib

Author : Ahmed Djebbar
ISBN : OCLC:949242899
Genre :
File Size : 56. 33 MB
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Growing Ideas Of Number

Author : John N. Crossley
ISBN : 9780864317094
Genre : Education
File Size : 73. 69 MB
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This book explores the notion of how number ideas, and ideas of number, have grown from ancient to modern times throughout history. It looks at how different types of number and views of numbers (and their meaning and applications) have varied across cutures over time, and combines historical consideration with the mathematics. The book illustrates some of the real problems and subtleties of number, including counting, calculation, measuring and using machines, which ancient and modern people have grappled with - and continue to do so today.

Memoir On The Theory Of The Partitions Of Numbers

Author : Percy Alexander Macmahon
ISBN : PRNC:32101065820407
Genre : Mathematics
File Size : 86. 35 MB
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