國立高雄大學圖資館 |

登入

回首頁

Mathematical phyllotaxis

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Mathematical phyllotaxisby Jonathan Swinton.
作者:	Swinton, Jonathan.
出版者:	Cham :Springer Nature Switzerland :2025.
面頁冊數:	xiv, 169 p. :ill. (chiefly col.), digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	PhyllotaxisMathematical models.
電子資源:	https://doi.org/10.1007/978-3-031-94013-2
ISBN:	9783031940132$q(electronic bk.)

Mathematical phyllotaxis
Swinton, Jonathan.

Mathematical phyllotaxis[electronic resource] /by Jonathan Swinton. - Cham :Springer Nature Switzerland :2025. - xiv, 169 p. :ill. (chiefly col.), digital ;24 cm. - Surveys and tutorials in the applied mathematical sciences,v. 172199-4773 ;. - Surveys and tutorials in the applied mathematical sciences ;v.7..

Motivation and outline -- Fibonacci numbers, the golden ratio, and co-prime integers -- Co-primality, continued fractions, and Möbius maps -- The geometry of cylindrical lattices -- Classifying cylindrical lattices -- Transformed Lattices -- Developmental biology of the plant -- Statisical phyllotaxis -- Placement models -- Stacked-disk models -- Some future directions.

For centuries, scientists and mathematicians have sought to explain why Fibonacci numbers appear in plant spirals. In recent decades, a modern consensus framework has emerged, offering a compelling mathematical and biological model that goes beyond Fibonacci structure to explain a variety of plant forms. This book provides a rigorous yet accessible introduction to that framework, spanning the mathematics of the Euclidean algorithm, bifurcation theory, and modern molecular biology. Delving into the mechanics of how plants determine organ placement, the book introduces key mathematical tools to classify and analyze these patterns. It examines classic and contemporary models, from Hofmeister's hypothesis to transporter protein-based auxin mechanisms, evaluating their current effectiveness in explaining the evolution and development of plant design. Written for mathematicians, biologists, and interdisciplinary researchers, Mathematics of Phyllotaxis equips readers with the knowledge to critique and contribute to this evolving field. Whether you're a student, a researcher, or simply fascinated by nature's mathematical beauty, this gorgeously illustrated book offers fresh insights into one of biology's most intriguing mysteries.

ISBN: 9783031940132$q(electronic bk.)

Standard No.: 10.1007/978-3-031-94013-2doiSubjects--Topical Terms:

1005062
Phyllotaxis
--Mathematical models.

LC Class. No.: QK649

Dewey Class. No.: 581.48

Mathematical phyllotaxis
LDR:02697nmm a22003495a 4500 001 689794
003 DE-He213
005 20251107114904.0
006 m d
007 cr nn 008maaau
008 260409s2025 sz s 0 eng d
020 $a 9783031940132$q(electronic bk.)
020 $a 9783031940125$q(paper)
024 7 $a 10.1007/978-3-031-94013-2 $2 doi
035 $a 978-3-031-94013-2
040 $a GP $c GP
041 0 $a eng
050 4 $a QK649
072 7 $a PBW $2 bicssc
072 7 $a PSA $2 bicssc
072 7 $a MAT003000 $2 bisacsh
072 7 $a PSAX $2 thema
082 0 4 $a 581.48 $2 23
090 $a QK649 $b .S979 2025
100 1 $a Swinton, Jonathan. $3 1005061
245 1 0 $a Mathematical phyllotaxis $h [electronic resource] / $c by Jonathan Swinton.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2025.
300 $a xiv, 169 p. : $b ill. (chiefly col.), digital ; $c 24 cm.
490 1 $a Surveys and tutorials in the applied mathematical sciences, $x 2199-4773 ; $v v. 17
505 0 $a Motivation and outline -- Fibonacci numbers, the golden ratio, and co-prime integers -- Co-primality, continued fractions, and Möbius maps -- The geometry of cylindrical lattices -- Classifying cylindrical lattices -- Transformed Lattices -- Developmental biology of the plant -- Statisical phyllotaxis -- Placement models -- Stacked-disk models -- Some future directions.
520 $a For centuries, scientists and mathematicians have sought to explain why Fibonacci numbers appear in plant spirals. In recent decades, a modern consensus framework has emerged, offering a compelling mathematical and biological model that goes beyond Fibonacci structure to explain a variety of plant forms. This book provides a rigorous yet accessible introduction to that framework, spanning the mathematics of the Euclidean algorithm, bifurcation theory, and modern molecular biology. Delving into the mechanics of how plants determine organ placement, the book introduces key mathematical tools to classify and analyze these patterns. It examines classic and contemporary models, from Hofmeister's hypothesis to transporter protein-based auxin mechanisms, evaluating their current effectiveness in explaining the evolution and development of plant design. Written for mathematicians, biologists, and interdisciplinary researchers, Mathematics of Phyllotaxis equips readers with the knowledge to critique and contribute to this evolving field. Whether you're a student, a researcher, or simply fascinated by nature's mathematical beauty, this gorgeously illustrated book offers fresh insights into one of biology's most intriguing mysteries.
650 0 $a Phyllotaxis $x Mathematical models. $3 1005062
650 0 $a Fibonacci numbers. $3 397259
650 1 4 $a Mathematical and Computational Biology. $3 514442
650 2 4 $a Applications of Mathematics. $3 273744
650 2 4 $a Plant Science. $3 911813
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Surveys and tutorials in the applied mathematical sciences ; $v v.7. $3 860019
856 4 0 $u https://doi.org/10.1007/978-3-031-94013-2
950 $a Mathematics and Statistics (SpringerNature-11649)