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Golden Angle
In geometry, the golden angle is the smaller of the two angles created by sectioning the circumference of a circle according to the golden ratio; that is, into two arcs such that the ratio of the length of the smaller arc to the length of the larger arc is the same as the ratio of the length of the larger arc to the full circumference of the circle. Algebraically, let ''a+b'' be the circumference of a circle, divided into a longer arc of length ''a'' and a smaller arc of length ''b'' such that : \frac = \frac The golden angle is then the angle subtended by the smaller arc of length ''b''. It measures approximately 137.5077640500378546463487 ...° or in radians 2.39996322972865332 ... . The name comes from the golden angle's connection to the golden ratio ''φ''; the exact value of the golden angle is : 360\left(1 - \frac\right) = 360(2 - \varphi) = \frac = 180(3 - \sqrt)\text or : 2\pi \left( 1 - \frac\right) = 2\pi(2 - \varphi) = \frac = \pi(3 - \sqrt)\text, wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Golden Angle
In geometry, the golden angle is the smaller of the two angles created by sectioning the circumference of a circle according to the golden ratio; that is, into two arcs such that the ratio of the length of the smaller arc to the length of the larger arc is the same as the ratio of the length of the larger arc to the full circumference of the circle. Algebraically, let ''a+b'' be the circumference of a circle, divided into a longer arc of length ''a'' and a smaller arc of length ''b'' such that : \frac = \frac The golden angle is then the angle subtended by the smaller arc of length ''b''. It measures approximately 137.5077640500378546463487 ...° or in radians 2.39996322972865332 ... . The name comes from the golden angle's connection to the golden ratio ''φ''; the exact value of the golden angle is : 360\left(1 - \frac\right) = 360(2 - \varphi) = \frac = 180(3 - \sqrt)\text or : 2\pi \left( 1 - \frac\right) = 2\pi(2 - \varphi) = \frac = \pi(3 - \sqrt)\text, wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sunflower Seed Pattern Animation
The common sunflower (''Helianthus annuus'') is a large annual forb of the genus ''Helianthus'' grown as a crop for its edible oily seeds. Apart from cooking oil production, it is also used as livestock forage (as a meal or a silage plant), as bird food, in some industrial applications, and as an ornamental in domestic gardens. Wild ''H. annuus'' is a widely branched annual plant with many flower heads. The domestic sunflower, however, often possesses only a single large inflorescence (flower head) atop an unbranched stem. The binomial name ''Helianthus annuus'' is derived from the Greek ''Helios'' 'sun' and ''anthos'' 'flower', while the epithet ''annuus'' means 'annual' in Latin. The plant was first domesticated in the Americas. Sunflower seeds were brought to Europe from the Americas in the 16th century, where, along with sunflower oil, they became a widespread cooking ingredient. With time, bulk of industrial-scale production has shifted to Eastern Europe, and () Russia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Golden Ratio
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0, where the Greek letter phi ( or \phi) denotes the golden ratio. The constant \varphi satisfies the quadratic equation \varphi^2 = \varphi + 1 and is an irrational number with a value of The golden ratio was called the extreme and mean ratio by Euclid, and the divine proportion by Luca Pacioli, and also goes by several other names. Mathematicians have studied the golden ratio's properties since antiquity. It is the ratio of a regular pentagon's diagonal to its side and thus appears in the construction of the dodecahedron and icosahedron. A golden rectangle—that is, a rectangle with an aspect ratio of \varphi—may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has been used to analyze the proportions of natural object ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''List of geometers, geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point (geometry), point, line (geometry), line, plane (geometry), plane, distance, angle, surface (mathematics), surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MathWorld
''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Digital Library grant to the University of Illinois at Urbana–Champaign. History Eric W. Weisstein, the creator of the site, was a physics and astronomy student who got into the habit of writing notes on his mathematical readings. In 1995 he put his notes online and called it "Eric's Treasure Trove of Mathematics." It contained hundreds of pages/articles, covering a wide range of mathematical topics. The site became popular as an extensive single resource on mathematics on the web. Weisstein continuously improved the notes and accepted corrections and comments from online readers. In 1998, he made a contract with CRC Press and the contents of the site were published in print and CD-ROM form, titled "CRC Concise Encyclopedia of Mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
137 (number)
137 (one hundred ndthirty-seven) is the natural number following 136 and preceding 138. In mathematics 137 is: * the 33rd prime number; the next is 139, with which it comprises a twin prime, and thus 137 is a Chen prime. * an Eisenstein prime with no imaginary part and a real part of the form 3n - 1. * the fourth Stern prime. * a Pythagorean prime: a prime number of the form 4''n'' + 1, where ''n'' = 34 (137 = 4x34 + 1) or the sum of two squares 112 + 42 (121 + 16). * a strong prime in the sense that it is more than the arithmetic mean of its two neighboring primes. * a strictly non-palindromic number and a primeval number. * a factor of 10001 (the other being 73) and the repdigit 11111111 (= 10001 × 1111). * using two radii to divide a circle according to the golden ratio yields sectors of approximately 137° (the golden angle) and 222°. * 1/137 = 0.007299270072992700..., so its period value is palindromic and has a period length of only 8. In physics * Since the e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parastichy
Parastichy, in phyllotaxy, is the spiral pattern of particular plant organs on some plants, such as areoles on cacti stems, florets in sunflower heads and scales in pine cones. These spirals involve the insertion of a single primordium. See also * Embryology * * Gerrit van Iterson * * 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 ... References External links Smith College Spiral Lattices & Parastichy Interactive Parastichies Explorer Plant morphology {{botany-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Primordia
A primordium (; plural: primordia; synonym: anlage) in embryology, is an Organ (anatomy), organ or tissue in its earliest recognizable stage of development. Cell (biology), Cells of the primordium are called primordial cells. A primordium is the simplest set of cells capable of triggering growth of the would-be organ and the initial foundation from which an organ is able to grow. In flowering plants, a floral primordium gives rise to a flower. Although it is a frequently used term in plant biology, the word is used in describing the biology of all multicellular organisms (for example: a tooth primordium in animals, a leaf primordium in plants or a sporocarp (fungi), sporophore primordium in fungi.) Primordium development in plants Plants produce both leaf and flower primordia cells at the shoot apical meristem (SAM). Primordium development in plants is critical to the proper positioning and development of plant organs and cells. The process of primordium development is intricat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sunflower
The common sunflower (''Helianthus annuus'') is a large annual forb of the genus ''Helianthus'' grown as a crop for its edible oily seeds. Apart from cooking oil production, it is also used as livestock forage (as a meal or a silage plant), as bird food, in some industrial applications, and as an ornamental in domestic gardens. Wild ''H. annuus'' is a widely branched annual plant with many flower heads. The domestic sunflower, however, often possesses only a single large inflorescence (flower head) atop an unbranched stem. The binomial name ''Helianthus annuus'' is derived from the Greek ''Helios'' 'sun' and ''anthos'' 'flower', while the epithet ''annuus'' means 'annual' in Latin. The plant was first domesticated in the Americas. Sunflower seeds were brought to Europe from the Americas in the 16th century, where, along with sunflower oil, they became a widespread cooking ingredient. With time, bulk of industrial-scale production has shifted to Eastern Europe, and () Russ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floret
This glossary of botanical terms is a list of definitions of terms and concepts relevant to botany and plants in general. Terms of plant morphology are included here as well as at the more specific Glossary of plant morphology and Glossary of leaf morphology. For other related terms, see Glossary of phytopathology, Glossary of lichen terms, and List of Latin and Greek words commonly used in systematic names. A B ... [...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] |
