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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 Arc (geometry), 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 ...° or in radians ... . 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, where the equivalences follow from ... [...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] |
Angle
In Euclidean geometry, an angle can refer to a number of concepts relating to the intersection of two straight Line (geometry), lines at a Point (geometry), point. Formally, an angle is a figure lying in a Euclidean plane, plane formed by two Ray (geometry), rays, called the ''Side (plane geometry), sides'' of the angle, sharing a common endpoint, called the ''vertex (geometry), vertex'' of the angle. More generally angles are also formed wherever two lines, rays or line segments come together, such as at the corners of triangles and other polygons. An angle can be considered as the region of the plane bounded by the sides. Angles can also be formed by the intersection of two planes or by two intersecting curves, in which case the rays lying tangent to each curve at the point of intersection define the angle. The term ''angle'' is also used for the size, magnitude (mathematics), magnitude or Physical quantity, quantity of these types of geometric figures and in this context an a ... [...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. 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 Mathematics''. The free online version became only partially accessible to the public. In 1999 Weisstein we ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci Sequence
In mathematics, the Fibonacci sequence is a sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted . Many writers begin the sequence with 0 and 1, although some authors start it from 1 and 1 and some (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the sequence begins : 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, also known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book . 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 Fi ... [...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 summation, sum to the larger of the two quantities. Expressed algebraically, for quantities and with , is in a golden ratio to if \frac = \frac = \varphi, where the Greek letter Phi (letter), phi ( or ) denotes the golden ratio. The constant satisfies the quadratic equation 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; it also goes by 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 Straightedge and compass construction, construction of the dodecahedron and icosahedron. A golden rectangle—that is, a rectangle with an aspect ratio of —may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has bee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
138 (number)
138 (one hundred [and] thirty-eight) is the natural number following 137 (number), 137 and preceding 139 (number), 139. Mathematics 138 is a sphenic number, an Ulam number, an abundant number, and a square-free congruent number. References [Baidu] |
137 (number)
137 (one hundred [and] thirty-seven) is the natural number following 136 (number), 136 and preceding 138 (number), 138. Mathematics 137 is: * the 33rd prime number; the next is 139 (number), 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 4n+1, where n=34 (137=4\times 34+1) or the sum of two squares 11^+4^ = (121+16). * a combination of three terms 4^+3^-2^ = (64+81-8), cube of 4 + Triangular number T4+T2 on each cube face (along 3 axes) - peaks (single 6th peak as free link) * 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 (number), 73) and the repdigit 11111111 (= 10001 × 1111). * using two radii to divide a circle according to the golden ratio ... [...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 {{plant-morphology-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci
Leonardo Bonacci ( – ), commonly known as Fibonacci, was an Italians, Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages". The name he is commonly called, ''Fibonacci'', is first found in a modern source in a 1838 text by the Franco-Italian mathematician Guglielmo Libri Carucci dalla Sommaja, Guglielmo Libri and is short for ('son of Bonacci'). However, even as early as 1506, Perizolo, a notary of the Holy Roman Empire, mentions him as "Lionardo Fibonacci". Fibonacci popularized the Hindu–Arabic numeral system, Indo–Arabic numeral system in the Western world primarily through his composition in 1202 of (''Book of Calculation'') and also introduced Europe to the sequence of Fibonacci numbers, which he used as an example in . Biography Fibonacci was born around 1170 to Guglielmo, an Italian merchant and customs official who directed a trading post in Béjaïa, Bugia, modern-day Béjaïa, Algeria ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Primordia
A primordium (; : primordia; synonym: anlage), in embryology, is an organ or tissue in its earliest recognizable stage of development. 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 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 intricately regulated by a set of genes that affect the posit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sunflower
The common sunflower (''Helianthus annuus'') is a species of large annual forb of the daisy family Asteraceae. The common sunflower is harvested for its edible oily seeds, which are often eaten as a snack food. They are also used in the production of cooking oil, as food for livestock, as bird food, and as plantings in domestic gardens for aesthetics. Wild plants are known for their multiple flower heads, whereas the domestic sunflower often possesses a single large flower head atop an unbranched stem. Description The plant has an erect rough-hairy stem, reaching typical heights of . The tallest sunflower on record achieved . Sunflower leaves are broad, coarsely toothed, rough and mostly alternate; those near the bottom are largest and commonly heart-shaped. Flower The plant flowers in summer. What is often called the " flower" of the sunflower is actually a "flower head" ( pseudanthium), wide, of numerous small individual five-petaled flowers (" florets"). The out ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
