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Solving The Riddle Of Phyllotaxis
''Solving the Riddle of Phyllotaxis: Why the Fibonacci Numbers and the Golden Ratio Occur in Plants'' is a book on the mathematics of plant structure, and in particular on phyllotaxis, the arrangement of leaves on plant stems. It was written by Irving Adler, and published in 2012 by World Scientific. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. Background Irving Adler (1913–2012) was known as a peace protester, schoolteacher, and children's science book author before, in 1961, earning a doctorate in abstract algebra. Even later in his life, Adler began working on phyllotaxis, the mathematical structure of leaves on plant stems. This book, which collects several of his papers on the subject previously published in journals and edited volumes, is the last of his 85 books to be published before his death. Topics Different plants arrange their leaves differently, for instance on alte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solving The Riddle Of Phyllotaxis
''Solving the Riddle of Phyllotaxis: Why the Fibonacci Numbers and the Golden Ratio Occur in Plants'' is a book on the mathematics of plant structure, and in particular on phyllotaxis, the arrangement of leaves on plant stems. It was written by Irving Adler, and published in 2012 by World Scientific. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. Background Irving Adler (1913–2012) was known as a peace protester, schoolteacher, and children's science book author before, in 1961, earning a doctorate in abstract algebra. Even later in his life, Adler began working on phyllotaxis, the mathematical structure of leaves on plant stems. This book, which collects several of his papers on the subject previously published in journals and edited volumes, is the last of his 85 books to be published before his death. Topics Different plants arrange their leaves differently, for instance on alte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circle Packing Theorem
The circle packing theorem (also known as the Koebe–Andreev–Thurston theorem) describes the possible tangency relations between circles in the plane whose interiors are disjoint. A circle packing is a connected collection of circles (in general, on any Riemann surface) whose interiors are disjoint. The intersection graph of a circle packing is the graph having a vertex for each circle, and an edge for every pair of circles that are tangent. If the circle packing is on the plane, or, equivalently, on the sphere, then its intersection graph is called a coin graph; more generally, intersection graphs of interior-disjoint geometric objects are called tangency graphs or contact graphs. Coin graphs are always connected, simple, and planar. The circle packing theorem states that these are the only requirements for a graph to be a coin graph: Circle packing theorem: For every connected simple planar graph ''G'' there is a circle packing in the plane whose intersection graph is (isom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Books
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci Numbers
In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the first few values in the sequence are: :0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. The Fibonacci numbers were first described in Indian mathematics, as early as 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths. They are named after the Italian mathematician Leonardo of Pisa, later known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book ''Liber Abaci''. Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the ''Fibonacci Quarterly''. Applications of Fibonacci numbers include co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plant Morphology
Phytomorphology is the study of the morphology (biology), physical form and external structure of plants.Raven, P. H., R. F. Evert, & S. E. Eichhorn. ''Biology of Plants'', 7th ed., page 9. (New York: W. H. Freeman, 2005). . This is usually considered distinct from plant anatomy, which is the study of the internal Anatomy, structure of plants, especially at the microscopic level. Plant morphology is useful in the visual identification of plants. Recent studies in molecular biology started to investigate the molecular processes involved in determining the conservation and diversification of plant morphologies. In these studies transcriptome conservation patterns were found to mark crucial ontogenetic transitions during the plant life cycle which may result in evolutionary constraints limiting diversification. Scope Plant morphology "represents a study of the development, form, and structure of plants, and, by implication, an attempt to interpret these on the basis of similarit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johannes Kepler
Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws of planetary motion, and his books ''Astronomia nova'', ''Harmonice Mundi'', and ''Epitome Astronomiae Copernicanae''. These works also provided one of the foundations for Newton's theory of universal gravitation. Kepler was a mathematics teacher at a seminary school in Graz, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to the astronomer Tycho Brahe in Prague, and eventually the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He also taught mathematics in Linz, and was an adviser to General Wallenstein. Additionally, he did fundamental work in the field of optics, invented an improved version of the refracting (or Keplerian) telescope, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonardo Da Vinci
Leonardo di ser Piero da Vinci (15 April 14522 May 1519) was an Italian polymath of the High Renaissance who was active as a painter, Drawing, draughtsman, engineer, scientist, theorist, sculptor, and architect. While his fame initially rested on his achievements as a painter, he also became known for #Journals and notes, his notebooks, in which he made drawings and notes on a variety of subjects, including anatomy, astronomy, botany, cartography, painting, and paleontology. Leonardo is widely regarded to have been a genius who epitomized the Renaissance humanism, Renaissance humanist ideal, and his List of works by Leonardo da Vinci, collective works comprise a contribution to later generations of artists matched only by that of his younger contemporary, Michelangelo. Born Legitimacy (family law), out of wedlock to a successful Civil law notary, notary and a lower-class woman in, or near, Vinci, Tuscany, Vinci, he was educated in Florence by the Italian painter and sculptor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theophrastus
Theophrastus (; grc-gre, Θεόφραστος ; c. 371c. 287 BC), a Greek philosopher and the successor to Aristotle in the Peripatetic school. He was a native of Eresos in Lesbos.Gavin Hardy and Laurence Totelin, ''Ancient Botany'', Routledge, 2015, p. 8. His given name was Tyrtamus (); his nickname (or 'godly phrased') was given by Aristotle, his teacher, for his "divine style of expression". He came to Athens at a young age and initially studied in Plato's school. After Plato's death, he attached himself to Aristotle who took to Theophrastus in his writings. When Aristotle fled Athens, Theophrastus took over as head of the Lyceum. Theophrastus presided over the Peripatetic school for thirty-six years, during which time the school flourished greatly. He is often considered the father of botany for his works on plants. After his death, the Athenians honoured him with a public funeral. His successor as head of the school was Strato of Lampsacus. The interests of Theophrastus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continued Fraction
In mathematics, a continued fraction is an expression (mathematics), expression obtained through an iterative process of representing a number as the sum of its integer part and the multiplicative inverse, reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on. In a finite continued fraction (or terminated continued fraction), the iteration/recursion is terminated after finitely many steps by using an integer in lieu of another continued fraction. In contrast, an infinite continued fraction is an infinite expression (mathematics), infinite expression. In either case, all integers in the sequence, other than the first, must be positive number, positive. The integers a_i are called the coefficients or terms of the continued fraction. It is generally assumed that the numerator of all of the fractions is 1. If arbitrary values and/or function (mathematics), functions are used in place of one or more of the numerat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Space-filling Curve
In mathematical analysis, a space-filling curve is a curve whose range contains the entire 2-dimensional unit square (or more generally an ''n''-dimensional unit hypercube). Because Giuseppe Peano (1858–1932) was the first to discover one, space-filling curves in the 2-dimensional plane are sometimes called ''Peano curves'', but that phrase also refers to the Peano curve, the specific example of a space-filling curve found by Peano. Definition Intuitively, a curve in two or three (or higher) dimensions can be thought of as the path of a continuously moving point. To eliminate the inherent vagueness of this notion, Jordan in 1887 introduced the following rigorous definition, which has since been adopted as the precise description of the notion of a ''curve'': In the most general form, the range of such a function may lie in an arbitrary topological space, but in the most commonly studied cases, the range will lie in a Euclidean space such as the 2-dimensional plane (a ''pla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adhemar Bultheel
Adhemar François Bultheel (born 1948) is a Belgian mathematician and computer scientist, the former president of the Belgian Mathematical Society. He is a prolific book reviewer for the Bulletin of the Belgian Mathematical Society and for the European Mathematical Society. His research concerns approximation theory. Education and career Bultheel was born in Zwijndrecht, Belgium on December 14, 1948. He earned a licenciate in mathematics in 1970 and another in industrial mathematics in 1971, both from KU Leuven KU Leuven (or Katholieke Universiteit Leuven) is a Catholic research university in the city of Leuven, Belgium. It conducts teaching, research, and services in computer science, engineering, natural sciences, theology, humanities, medicine, l .... He remained at KU Leuven for a bachelor's degree in 1975 and a PhD in mathematics in 1979. His dissertation, ''Recursive Rational Approximation'', was jointly supervised by Patrick M. Dewilde and Hugo Van de Vel. Except for a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phyllotaxis
In botany, phyllotaxis () or phyllotaxy is the arrangement of leaf, leaves on a plant stem. Phyllotactic spirals form a distinctive class of patterns in nature. Leaf arrangement The basic leaf#Arrangement on the stem, arrangements of leaves on a stem are opposite and alternate (also known as spiral). Leaves may also be Whorl (botany), whorled if several leaves arise, or appear to arise, from the same level (at the same Node (botany), node) on a stem. With an opposite leaf arrangement, two leaves arise from the stem at the same level (at the same Node (botany), node), on opposite sides of the stem. An opposite leaf pair can be thought of as a whorl of two leaves. With an alternate (spiral) pattern, each leaf arises at a different point (node) on the stem. Distichous phyllotaxis, also called "two-ranked leaf arrangement" is a special case of either opposite or alternate leaf arrangement where the leaves on a stem are arranged in two vertical columns on opposite sides of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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