In vascular plants, the root is the organ of a plant that typically lies below the surface of the soil. Roots can also be aerial or aerating, that is, growing up above the ground or especially above water. Furthermore, a stem normally occurring below ground is not exceptional either (see rhizome). Therefore, the root is best defined as the non-leaf, non-nodes bearing parts of the plant's body. However, important internal structural differences between stems and roots exist.

Primary and secondary cotton roots
Primary and secondary roots in a cotton plant

Evolutionary history

The fossil record of roots—or rather, infilled voids where roots rotted after death—spans back to the late Silurian, about 430 million years ago.[1] Their identification is difficult, because casts and molds of roots are so similar in appearance to animal burrows. They can be discriminated using a range of features.[2]


The first root that comes from a plant is called the radicle. A root's four major functions are:

  1. absorption of water and inorganic nutrients;
  2. anchoring of the plant body to the ground, and supporting it;
  3. storage of food and nutrients;
  4. vegetative reproduction and competition with other plants.

In response to the concentration of nutrients, roots also synthesise cytokinin, which acts as a signal as to how fast the shoots can grow. Roots often function in storage of food and nutrients. The roots of most vascular plant species enter into symbiosis with certain fungi to form mycorrhizae, and a large range of other organisms including bacteria also closely associate with roots.

Kiental entre Herrsching y Andechs, Alemania 2012-05-01, DD 12
Large, mature tree roots above the soil


CSIRO ScienceImage 11626 Barley root
The cross-section of a barley root

When dissected, the arrangement of the cells in a root is root hair, epidermis, epiblem, cortex, endodermis, pericycle and, lastly, the vascular tissue in the centre of a root to transport the water absorbed by the root to other places of the plant.

Ranunculus Root Cross Section
Ranunculus Root Cross Section

Perhaps the most striking characteristic of roots (that makes it distinguishable from other plant organs such as stem-branches and leaves) is that, roots have an endogenous[3] origin, i.e. it originates and develops from an inner layer of the mother axis (Such as Pericycle[4]). Whereas Stem-branching and leaves (those develop as buds) are exogenous, i.e. start to develop from the cortex, an outer layer.


In its simplest form, the term root architecture refers to the spatial configuration of a plant’s root system. This system can be extremely complex and is dependent upon multiple factors such as the species of the plant itself, the composition of the soil and the availability of nutrients.[5]

The configuration of root systems serves to structurally support the plant, compete with other plants and for uptake of nutrients from the soil.[6] Roots grow to specific conditions, which, if changed, can impede a plant's growth. For example, a root system that has developed in dry soil may not be as efficient in flooded soil, yet plants are able to adapt to other changes in the environment, such as seasonal changes.[6]

Root architecture plays the important role of providing a secure supply of nutrients and water as well as anchorage and support. The main terms used to classify the architecture of a root system are:[7]

  • Branch magnitude: the number of links (exterior or interior).
  • Topology: the pattern of branching, including:
  1. Herringbone: alternate lateral branching off a parent root
  2. Dichotomous: opposite, forked branches
  3. Radial: whorl(s) of branches around a root
  • Link length: the distance between branches.
  • Root angle: the radial angle of a lateral root’s base around the parent root’s circumference, the angle of a lateral root from its parent root, and the angle an entire system spreads.
  • Link radius: the diameter of a root.

All components of the root architecture are regulated through a complex interaction between genetic responses and responses due to environmental stimuli. These developmental stimuli are categorised as intrinsic, the genetic and nutritional influences, or extrinsic, the environmental influences and are interpreted by signal transduction pathways.[8] The extrinsic factors that affect root architecture include gravity, light exposure, water and oxygen, as well as the availability or lack of nitrogen, phosphorus, sulphur, aluminium and sodium chloride. The main hormones (intrinsic stimuli) and respective pathways responsible for root architecture development include:

  • Auxin – Auxin promotes root initiation, root emergence and primary root elongation.
  • Cytokinins – Cytokinins regulate root apical meristem size and promote lateral root elongation.
  • Gibberellins – Together with ethylene they promote crown primordia growth and elongation. Together with auxin they promote root elongation. Gibberellins also inhibit lateral root primordia initiation.
  • Ethylene – Ethylene promotes crown root formation.


Root of a Tree
Roots of trees

Early root growth is one of the functions of the apical meristem located near the tip of the root. The meristem cells more or less continuously divide, producing more meristem, root cap cells (these are sacrificed to protect the meristem), and undifferentiated root cells. The latter become the primary tissues of the root, first undergoing elongation, a process that pushes the root tip forward in the growing medium. Gradually these cells differentiate and mature into specialized cells of the root tissues.[9]

Growth from apical meristems is known as primary growth, which encompasses all elongation. Secondary growth encompasses all growth in diameter, a major component of woody plant tissues and many nonwoody plants. For example, storage roots of sweet potato have secondary growth but are not woody. Secondary growth occurs at the lateral meristems, namely the vascular cambium and cork cambium. The former forms secondary xylem and secondary phloem, while the latter forms the periderm.

In plants with secondary growth, the vascular cambium, originating between the xylem and the phloem, forms a cylinder of tissue along the stem and root. The vascular cambium forms new cells on both the inside and outside of the cambium cylinder, with those on the inside forming secondary xylem cells, and those on the outside forming secondary phloem cells. As secondary xylem accumulates, the "girth" (lateral dimensions) of the stem and root increases. As a result, tissues beyond the secondary phloem including the epidermis and cortex, in many cases tend to be pushed outward and are eventually "sloughed off" (shed).

At this point, the cork cambium begins to form the periderm, consisting of protective cork cells containing suberin. In roots, the cork cambium originates in the pericycle, a component of the vascular cylinder.

The vascular cambium produces new layers of secondary xylem annually. The xylem vessels are dead at maturity but are responsible for most water transport through the vascular tissue in stems and roots.

Tree roots usually grow to three times the diameter of the branch spread, only half of which lie underneath the trunk and canopy. The roots from one side of a tree usually supply nutrients to the foliage on the same side. Some families however, such as Sapindaceae (the maple family), show no correlation between root location and where the root supplies nutrients on the plant.


There is a correlation of roots using the process of plant perception to sense their physical environment to grow,[10] including the sensing of light,[11] and physical barriers. Over time, roots can crack foundations, snap water lines, and lift sidewalks. Research has shown that roots have ability to recognize 'self' and 'non-self' roots in same soil environment.[12]

The correct environment of air, mineral nutrients and water directs plant roots to grow in any direction to meet the plant's needs. Roots will shy or shrink away from dry[13] or other poor soil conditions.

Gravitropism directs roots to grow downward at germination, the growth mechanism of plants that also causes the shoot to grow upward.[14]

Fluorescent imaging of an emerging lateral root.

Shade Avoidance Root Response

In order to avoid shade, plants utilize a shade avoidance response. When a plant is under dense vegetation, the presence of other vegetation nearby will cause the plant to avoid lateral growth and experience an increase in upward shoot, as well as downward root growth. In order to escape shade, plants adjust their root architecture, most notably by decreasing the length and amount of lateral roots emerging from the primary root. Experimentation of mutant variants of Arabidospis thaliana found that plants sense the Red to Far Red light ratio that enters the plant through photoreceptors known as phytochromes.[15] Nearby plant leaves will absorb red light and reflect far- red light which will cause the ratio red to far red light to lower. The phytochrome PhyA that senses this Red to Far Red light ratio is localized in both the root system as well as the shoot system of plants, but through knockout mutant experimentation, it was found that root localized PhyA does not sense the light ratio, whether directly or axially, that leads to changes in the lateral root architecture.[15] Research instead found that shoot localized PhyA is the phytochrome responsible for causing these architectural changes of the lateral root. Research has also found that phytochrome completes these architectural changes through the manipulation of auxin distribution in the root of the plant.[15] When a low enough Red to Far Red ratio is sensed by PhyA, the phyA in the shoot will be mostly in its active form.[16] In this form, PhyA stabilize the transcription factor HY5 causing it to no longer be degraded as it is when phyA is in its inactive form. This stabilized transcription factor is then able to be transported to the roots of the plant through the phloem, where it proceeds to induce its own transcription as a way to amplify its signal. In the roots of the plant HY5 functions to inhibit an auxin response factor known as ARF19, a response factor responsible for the translation of PIN3 and LAX3, two well known auxin transporting proteins.[16] Thus, through manipulation of ARF19, the level and activity of auxin transporters PIN3 and LAX3 is inhibited.[16] Once inhibited, auxin levels will be low in areas where lateral root emergence normally occurs, resulting in a failure for the plant to have the emergence of the lateral root primordium through the root pericycle. With this complex manipulation of Auxin transport in the roots, lateral root emergence will be inhibited in the roots and the root will instead elongate downwards, promoting vertical plant growth in an attempt to avoid shade.[15][16]

Research of Arabidopsis has led to the discovery of how this auxin mediated root response works. In an attempt to discover the role that phytochrome plays in lateral root development, Salisbury et al. (2007) worked with Arabidopsis thaliana grown on agar plates. Salisbury et al. used wild type plants along with varying protein knockout and gene knockout Arabidopsis mutants to observe the results these mutations had on the root architecture, protein presence, and gene expression. To do this, Salisbury et al. used GFP fluorescence along with other forms of both macro and microscopic imagery to observe any changes various mutations caused. From these research, Salisbury et al. were able to theorize that shoot located phytochromes alter auxin levels in roots, controlling lateral root development and overall root architecture.[15] In the experiments of van Gelderen et al. (2018), they wanted to see if and how it is that the shoot of Arabidopsis thaliana alters and affects root development and root architecture. To do this, they took Arabidopsis plants, grew them in agar gel, and exposed the roots and shoots to separate sources of light. From here, they altered the different wavelengths of light the shoot and root of the plants were receiving and recorded the lateral root density, amount of lateral roots, and the general architecture of the lateral roots. To identify the function of specific photoreceptors, proteins, genes, and hormones, they utilized various Arabidopsis knockout mutants and observed the resulting changes in lateral roots architecture. Through their observations and various experiments, van Gelderen et al. were able to develop a mechanism for how root detection of Red to Far-red light ratios alter lateral root development.[16]


A true root system consists of a primary root and secondary roots (or lateral roots).

  • the diffuse root system: the primary root is not dominant; the whole root system is fibrous and branches in all directions. Most common in monocots. The main function of the fibrous root is to anchor the plant.


Prop roots of Maize plant
Stilt roots of Maize plant
Adventitious roots on Odontonema aka Firespike
Roots forming above ground on a cutting of an Odontonema ("Firespike")
Aerating roots of a mangrove
Root tip
The growing tip of a fine root
Aerial root
Aerial root
Socratea exorriza2002 03 12
The stilt roots of Socratea exorrhiza
Visible roots
Visible roots

The roots, or parts of roots, of many plant species have become specialized to serve adaptive purposes besides the two primary functions, described in the introduction.

  • Adventitious roots arise out-of-sequence from the more usual root formation of branches of a primary root, and instead originate from the stem, branches, leaves, or old woody roots. They commonly occur in monocots and pteridophytes, but also in many dicots, such as clover (Trifolium), ivy (Hedera), strawberry (Fragaria) and willow (Salix). Most aerial roots and stilt roots are adventitious. In some conifers adventitious roots can form the largest part of the root system.
  • Aerating roots (or knee root or knee or pneumatophores or Cypress knee): roots rising above the ground, especially above water such as in some mangrove genera (Avicennia, Sonneratia). In some plants like Avicennia the erect roots have a large number of breathing pores for exchange of gases.
  • Aerial roots: roots entirely above the ground, such as in ivy (Hedera) or in epiphytic orchids. Many aerial roots are used to receive water and nutrient intake directly from the air - from fogs, dew or humidity in the air.[17] Some rely on leaf systems to gather rain or humidity and even store it in scales or pockets. Other aerial roots, such as mangrove aerial roots, are used for aeration and not for water absorption. Other aerial roots are used mainly for structure, functioning as prop roots, as in maize or anchor roots or as the trunk in strangler fig. In some Epiphytes - plants living above the surface on other plants, aerial roots serve for reaching to water sources or reaching the surface, and then functioning as regular surface roots.[17]
  • Contractile roots: these pull bulbs or corms of monocots, such as hyacinth and lily, and some taproots, such as dandelion, deeper in the soil through expanding radially and contracting longitudinally. They have a wrinkled surface.[18]
  • Coarse roots: roots that have undergone secondary thickening and have a woody structure. These roots have some ability to absorb water and nutrients, but their main function is transport and to provide a structure to connect the smaller diameter, fine roots to the rest of the plant.
  • Dimorphic root systems: roots with two distinctive forms for two separate functions
  • Fine roots: typically primary roots <2 mm diameter that have the function of water and nutrient uptake. They are often heavily branched and support mycorrhizas. These roots may be short lived, but are replaced by the plant in an ongoing process of root 'turnover'.
  • Haustorial roots: roots of parasitic plants that can absorb water and nutrients from another plant, such as in mistletoe (Viscum album) and dodder.
  • Propagative roots: roots that form adventitious buds that develop into aboveground shoots, termed suckers, which form new plants, as in Canada thistle, cherry and many others.
  • Proteoid roots or cluster roots: dense clusters of rootlets of limited growth that develop under low phosphate or low iron conditions in Proteaceae and some plants from the following families Betulaceae, Casuarinaceae, Elaeagnaceae, Moraceae, Fabaceae and Myricaceae.
  • Stilt roots: these are adventitious support roots, common among mangroves. They grow down from lateral branches, branching in the soil.
  • Storage roots: these roots are modified for storage of food or water, such as carrots and beets. They include some taproots and tuberous roots.
  • Structural roots: large roots that have undergone considerable secondary thickening and provide mechanical support to woody plants and trees.
  • Surface roots: these proliferate close below the soil surface, exploiting water and easily available nutrients. Where conditions are close to optimum in the surface layers of soil, the growth of surface roots is encouraged and they commonly become the dominant roots.
  • Tuberous roots: fleshy and enlarged lateral roots for food or water storage, e.g. sweet potato. A type of storage root distinct from taproot.


Exposed mango tree roots
Cross section of a mango tree

The distribution of vascular plant roots within soil depends on plant form, the spatial and temporal availability of water and nutrients, and the physical properties of the soil. The deepest roots are generally found in deserts and temperate coniferous forests; the shallowest in tundra, boreal forest and temperate grasslands. The deepest observed living root, at least 60 metres below the ground surface, was observed during the excavation of an open-pit mine in Arizona, USA. Some roots can grow as deep as the tree is high. The majority of roots on most plants are however found relatively close to the surface where nutrient availability and aeration are more favourable for growth. Rooting depth may be physically restricted by rock or compacted soil close below the surface, or by anaerobic soil conditions.

Depth records

Species Location Maximum rooting depth (m) References[19][20]
Boscia albitrunca Kalahari desert 68 Jennings (1974)
Juniperus monosperma Colorado Plateau 61 Cannon (1960)
Eucalyptus sp. Australian forest 61 Jennings (1971)
Acacia erioloba Kalahari desert 60 Jennings (1974)
Prosopis juliflora Arizona desert 53.3 Phillips (1963)

Environmental interactions

Certain plants, namely Fabaceae, form root nodules in order to associate and form a symbiotic relationship with nitrogen-fixing bacteria called rhizobia. Due to the high energy required to fix nitrogen from the atmosphere, the bacteria take carbon compounds from the plant to fuel the process. In return, the plant takes nitrogen compounds produced from ammonia by the bacteria.[21]

Economic importance

Roots and Soil Erosion
Roots can also protect the environment by holding the soil to reduce soil erosion

The term root crops refers to any edible underground plant structure, but many root crops are actually stems, such as potato tubers. Edible roots include cassava, sweet potato, beet, carrot, rutabaga, turnip, parsnip, radish, yam and horseradish. Spices obtained from roots include sassafras, angelica, sarsaparilla and licorice.

Sugar beet is an important source of sugar. Yam roots are a source of estrogen compounds used in birth control pills. The fish poison and insecticide rotenone is obtained from roots of Lonchocarpus spp. Important medicines from roots are ginseng, aconite, ipecac, gentian and reserpine. Several legumes that have nitrogen-fixing root nodules are used as green manure crops, which provide nitrogen fertilizer for other crops when plowed under. Specialized bald cypress roots, termed knees, are sold as souvenirs, lamp bases and carved into folk art. Native Americans used the flexible roots of white spruce for basketry.

Tree roots can heave and destroy concrete sidewalks and crush or clog buried pipes.[22] The aerial roots of strangler fig have damaged ancient Mayan temples in Central America and the temple of Angkor Wat in Cambodia.

Trees stabilize soil on a slope prone to landslides. The root hairs work as an anchor on the soil.

Vegetative propagation of plants via cuttings depends on adventitious root formation. Hundreds of millions of plants are propagated via cuttings annually including chrysanthemum, poinsettia, carnation, ornamental shrubs and many houseplants.

Roots can also protect the environment by holding the soil to reduce soil erosion. This is especially important in areas such as sand dunes.

Roots on onion bulbs

See also


  1. ^ Retallack, G. J. (1986). "The fossil record of soils" (PDF). In Wright, V. P. (ed.). Paleosols: their Recognition and Interpretation. Oxford: Blackwell. pp. 1–57. Archived (PDF) from the original on 2017-01-07.
  2. ^ Hillier, R.; Edwards, D.; Morrissey, L.B. (2008). "Sedimentological evidence for rooting structures in the Early Devonian Anglo–Welsh Basin (UK), with speculation on their producers". Palaeogeography, Palaeoclimatology, Palaeoecology. 270 (3–4): 366–380. doi:10.1016/j.palaeo.2008.01.038.
  3. ^ College Botany, Volume-1 by HC Gangulee, KS Das and CT Datta, revised by S Sen, New Central Book Agency, Kolkata
  4. ^ BOTANY For Degree Students, 6th Ed, by AC Dutta, Revised by TC Dutta. Oxford University Press
  5. ^ Malamy, J. E. (2005). "Intrinsic and environmental response pathways that regulate root system architecture". Plant, Cell & Environment. 28: 67–77. doi:10.1111/j.1365-3040.2005.01306.x.
  6. ^ a b Caldwell, M. M.; Dawson, T. E.; Richards, J. H. (1998). "Hydraulic lift: consequences of water efflux from the roots of plants". Oecologia. 113 (2): 151–161. Bibcode:1998Oecol.113..151C. doi:10.1007/s004420050363. PMID 28308192.
  7. ^ Fitter, A. H (1991). "The ecological significance of root system architecture: an economic approach". In Atkinson, D. (ed.). Plant Root Growth: An Ecological Perspective. Blackwell. pp. 229–243.
  8. ^ Malamy, J. E.; Ryan K. S. (2001). "Environmental regulation of lateral root initiation in Arabidopsis". Plant Physiology. 127 (3): 899–909. doi:10.1104/pp.010406. PMC 129261. PMID 11706172.
  9. ^ Russell, P.J.; Hertz, P.E.; McMillan, B. (2013). Biology: The Dynamic Science. Cengage Learning. p. 750. ISBN 978-1-285-41534-5. Archived from the original on 2018-01-21. Retrieved 2017-04-24.
  10. ^ Nakagawa, Y.; Katagiri, T.; Shinozaki, K.; Qi, Z.; Tatsumi, H.; Furuichi, T.; Kishigami, A.; Sokabe, M.; Kojima, I.; Sato, S.; Kato, T.; Tabata, S.; Iida, K.; Terashima, A.; Nakano, M.; Ikeda, M.; Yamanaka, T.; Iida, H. (2007). "Arabidopsis plasma membrane protein crucial for Ca2+ influx and touch sensing in roots". Proceedings of the National Academy of Sciences. 104 (9): 3639–3644. Bibcode:2007PNAS..104.3639N. doi:10.1073/pnas.0607703104. PMC 1802001. PMID 17360695.
  11. ^ UV-B light sensing mechanism discovered in plant roots, San Francisco State University, December 8, 2008
  12. ^ HODGE, ANGELA (June 2009). "Root decisions". Plant, Cell & Environment. 32 (6): 628–640. doi:10.1111/j.1365-3040.2008.01891.x. ISSN 0140-7791. PMID 18811732.
  13. ^ Carminati, Andrea; Vetterlein, Doris; Weller, Ulrich; Vogel, Hans-Jörg; Oswald, Sascha E. (2009). "When roots lose contact". Vadose Zone Journal. 8 (3): 805–809. doi:10.2136/vzj2008.0147.
  14. ^ Chen, Rosen & Masson, 1999, p. 343.
  15. ^ a b c d e Salisbury, Frances J.; Hall, Anthony; Grierson, Claire S.; Halliday, Karen J. (2007-04-05). "Phytochrome coordinates Arabidopsis shoot and root development". The Plant Journal. 50 (3): 429–438. doi:10.1111/j.1365-313x.2007.03059.x. ISSN 0960-7412.
  16. ^ a b c d e Gelderen, Kasper van; Kang, Chiakai; Paalman, Richard; Keuskamp, Diederik; Hayes, Scott; Pierik, Ronald (2018-01-01). "Far-Red Light Detection in the Shoot Regulates Lateral Root Development through the HY5 Transcription Factor". The Plant Cell. 30 (1): 101–116. doi:10.1105/tpc.17.00771. PMC 5810572. PMID 29321188.
  17. ^ a b Nowak, Edward J.; Martin, Craig E. (1997). "Physiological and anatomical responses to water deficits in the CAM epiphyte Tillandsia ionantha (Bromeliaceae)". International Journal of Plant Sciences. 158 (6): 818–826. doi:10.1086/297495. JSTOR 2475361.
  18. ^ Pütz, Norbert (2002). "Contractile roots". In Waisel Y.; Eshel A.; Kafkafi U. (eds.). Plant roots: The hidden half (3rd ed.). New York: Marcel Dekker. pp. 975–987.
  19. ^ Canadell, J.; Jackson, R. B.; Ehleringer, J. B.; Mooney, H. A.; Sala, O. E.; Schulze, E.-D. (December 3, 2004). "Maximum rooting depth of vegetation types at the global scale". Oecologia. 108 (4): 583–595. Bibcode:1996Oecol.108..583C. doi:10.1007/BF00329030. PMID 28307789.
  20. ^ Stonea, E. L.; P. J. Kaliszb (1 December 1991). "On the maximum extent of tree roots". Forest Ecology and Management. 46 (1–2): 59–102. doi:10.1016/0378-1127(91)90245-Q.
  21. ^ Postgate, J. (1998). Nitrogen Fixation (3rd ed.). Cambridge, UK: Cambridge University Press.
  22. ^ Zahniser, David (February 21, 2008) "City to pass the bucks on sidewalks?" Archived 2015-04-17 at the Wayback Machine Los Angeles Times


  • Dennis D.Baldocchi and Liukang Xu. 2007. What limits evaporation from Mediterranean oak woodlands – The supply of moisture in the soil, physiological control by plants or the demand by the atmosphere? Vol 30, issue 10. Elsevier
  • Brundrett, M. C. (2002). "Coevolution of roots and mycorrhizas of land plants". New Phytologist. 154 (2): 275–304. doi:10.1046/j.1469-8137.2002.00397.x.
  • Chen, R.; Rosen, E.; Masson, P. H. (1999). "Gravitropism in Higher Plants". Plant Physiology. 120 (2): 343–350. doi:10.1104/pp.120.2.343. PMC 1539215. PMID 11541950. – article about how the roots sense gravity.
  • Clark, Lynn. 2004. Primary Root Structure and Development – lecture notes
  • Coutts, M. P. (1987). "Developmental processes in tree root systems". Canadian Journal of Forest Research. 17 (8): 761–767. doi:10.1139/x87-122.
  • Raven, J. A., D. Edwards. 2001. Roots: evolutionary origins and biogeochemical significance. Journal of Experimental Botany 52 (Suppl 1): 381–401. (Available online: Abstract | Full text (HTML) | Full text (PDF))
  • Schenk, H. J.; Jackson, R. B. (2002). "The global biogeography of roots". Ecological Monographs. 72 (3): 311–328. doi:10.2307/3100092. JSTOR 3100092.
  • Sutton, R. F.; Tinus, R. W. (1983). "Root and root system terminology". Forest Science Monograph. 24: 137.
  • Phillips, W. S. (1963). "Depth of roots in soil". Ecology. 44 (2): 424. doi:10.2307/1932198. JSTOR 1932198.
  • Caldwell, M. M., Dawson, T. E., & Richards, J. H. (1998). Hydraulic lift: consequences of water efflux from the roots of plants. Oecologia, 113(2), 151-161.

External links


1 (one, also called unit, unity, and (multiplicative) identity) is a number, numeral, and glyph. It represents a single entity, the unit of counting or measurement. For example, a line segment of unit length is a line segment of length 1. It is also the first of the infinite sequence of natural numbers, followed by 2.


The amplitude of a periodic variable is a measure of its change over a single period (such as time or spatial period). There are various definitions of amplitude (see below), which are all functions of the magnitude of the difference between the variable's extreme values. In older texts the phase is sometimes called the amplitude.


The beetroot is the taproot portion of a beet plant, usually known in North America as the beet, and also known as the table beet, garden beet, red beet, or golden beet. It is one of several cultivated varieties of Beta vulgaris grown for their edible taproots and leaves (called beet greens); they have been classified as B. vulgaris subsp. vulgaris 'Conditiva' Group.Besides being used as a food, beets have uses as a food colouring and as a medicinal plant. Many beet products are made from other Beta vulgaris varieties, particularly sugar beet.


Manihot esculenta, commonly called cassava (), manioc, yuca, macaxeira, mandioca and aipim is a woody shrub native to South America of the spurge family, Euphorbiaceae. Although a perennial plant, cassava is extensively cultivated as an annual crop in tropical and subtropical regions for its edible starchy tuberous root, a major source of carbohydrates. Though it is often called yuca in Latin American Spanish and in the United States, it is not related to yucca, a shrub in the family Asparagaceae. Cassava is predominantly consumed in boiled form, but substantial quantities are used to extract cassava starch, called tapioca, which is used for food, animal feed and industrial purposes. The Brazilian farinha, and the related garri of Western Africa, is an edible coarse flour obtained by grating cassava roots, pressing moisture off the obtained grated pulp, and finally drying it (and roasting in the case of farinha).

Cassava is the third-largest source of food carbohydrates in the tropics, after rice and maize. Cassava is a major staple food in the developing world, providing a basic diet for over half a billion people. It is one of the most drought-tolerant crops, capable of growing on marginal soils. Nigeria is the world's largest producer of cassava, while Thailand is the largest exporter of cassava starch.

Cassava is classified as either sweet or bitter. Like other roots and tubers, both bitter and sweet varieties of cassava contain antinutritional factors and toxins, with the bitter varieties containing much larger amounts. It must be properly prepared before consumption, as improper preparation of cassava can leave enough residual cyanide to cause acute cyanide intoxication, goiters, and even ataxia, partial paralysis, or death. The more toxic varieties of cassava are a fall-back resource (a "food security crop") in times of famine or food insecurity in some places. Farmers often prefer the bitter varieties because they deter pests, animals, and thieves.


Common chicory, Cichorium intybus, is a somewhat woody, perennial herbaceous plant of the dandelion family Asteraceae, usually with bright blue flowers, rarely white or pink. Many varieties are cultivated for salad leaves, chicons (blanched buds), or roots (var. sativum), which are baked, ground, and used as a coffee substitute and food additive. In the 21st century, inulin, an extract from chicory root, has been used in food manufacturing as a sweetener and source of dietary fiber.Chicory is grown as a forage crop for livestock. It lives as a wild plant on roadsides in its native Europe, and is now common in North America, China, and Australia, where it has become widely naturalized. "Chicory" is also the common name in the United States for curly endive (Cichorium endivia); these two closely related species are often confused.


Ginger (Zingiber officinale) is a flowering plant whose rhizome, ginger root or ginger, is widely used as a spice and a folk medicine. It is a herbaceous perennial which grows annual pseudostems (false stems made of the rolled bases of leaves) about a meter tall bearing narrow leaf blades. The inflorescences bear pale yellow with purple flowers and arise directly from the rhizome on separate shoots.Ginger is in the family Zingiberaceae, to which also belong turmeric (Curcuma longa), cardamom (Elettaria cardamomum), and galangal. Ginger originated in Island Southeast Asia and was likely domesticated first by the Austronesian peoples. It was transported with them throughout the Indo-Pacific during the Austronesian expansion (c. 5,000 BP), reaching as far as Hawaii. Ginger was also one of the first spices exported from the Orient, ginger arrived in Europe during the spice trade, and was used by ancient Greeks and Romans. The distantly related dicots in the genus Asarum are commonly called wild ginger because of their similar taste.


Liquorice (British English) or licorice (American English) ( LIK-ər-is(h)) is the root of Glycyrrhiza glabra from which a sweet flavour can be extracted. The liquorice plant is a herbaceous perennial legume native to the Middle East, southern Europe, and parts of Asia, such as India. It is not botanically related to anise, star anise, or fennel, which are sources of similar flavouring compounds. Liquorice flavours are used as candies or sweeteners, particularly in some European and Middle Eastern countries.

Liquorice extracts have been used in herbalism and traditional medicine. Excessive consumption of liquorice (more than 2 mg/kg/day of pure glycyrrhizinic acid, a liquorice component) may result in adverse effects, such as hypokalemia, increased blood pressure, and muscle weakness.

Newton's method

In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function.

The most basic version starts with a single-variable function f defined for a real variable x, the function's derivative f ′, and an initial guess x0 for a root of f. If the function satisfies necessary assumptions and the initial guess is close, then a better approximation x1 is

Geometrically, (x1, 0) is the intersection of the x-axis and the tangent of the graph of f at (x0, f (x0)): that is, the improved guess is the unique root of the

linear approximation at the initial point.

The process is repeated as

until a sufficiently accurate value is reached.

This algorithm is first in the class of Householder's methods, succeeded by Halley's method. The method can also be extended to complex functions and to systems of equations.


Parsley or garden parsley (Petroselinum crispum) is a species of flowering plant in the family Apiaceae that is native to the central Mediterranean region (Cyprus, southern Italy, Greece, Portugal, Spain, Malta, Morocco, Algeria, and Tunisia), but has naturalized elsewhere in Europe, and is widely cultivated as a herb, a spice, and a vegetable.

Where it grows as a biennial, in the first year, it forms a rosette of tripinnate leaves, 10–25 cm (3.9–9.8 in) long, with numerous 1–3 cm (0.4–1.2 in) leaflets and a taproot used as a food store over the winter. In the second year, it grows a flowering stem with sparser leaves and umbels with yellow to yellowish-green flowers.

Parsley is widely used in European, Middle Eastern, and American cuisine. Curly leaf parsley is often used as a garnish. In central Europe, eastern Europe, and southern Europe, as well as in western Asia, many dishes are served with fresh green chopped parsley sprinkled on top. Flat leaf parsley is similar, but it is easier to cultivate, and some say it has a stronger flavor. Root parsley is very common in central, eastern, and southern European cuisines, where it is used as a snack or a vegetable in many soups, stews, and casseroles.


Lophophora williamsii () or peyote () is a small, spineless cactus with psychoactive alkaloids, particularly mescaline. Peyote is a Spanish word derived from the Nahuatl, or Aztec, peyōtl [ˈpejoːt͡ɬ], meaning "glisten" or "glistening". Other sources translate the Nahuatl word as "Divine Messenger". Peyote is native to Mexico and southwestern Texas. It is found primarily in the Chihuahuan Desert and in the states of Coahuila, Nuevo León, Tamaulipas, and San Luis Potosí among scrub. It flowers from March to May, and sometimes as late as September. The flowers are pink, with thigmotactic anthers (like Opuntia).

Known for its psychoactive properties when ingested, peyote is used worldwide, having a long history of ritualistic and medicinal use by indigenous North Americans. Peyote contains the hallucinogen mescaline.


A polymath (Greek: πολυμαθής, polymathēs, "having learned much"; Latin: homo universalis, "universal man") is a person whose expertise spans a significant number of subject areas, known to draw on complex bodies of knowledge to solve specific problems.

In Western Europe, the first work to use polymathy in its title (De Polymathia tractatio: integri operis de studiis veterum) was published in 1603 by Johann von Wowern (de), a Hamburg philosopher.Von Wowern defined polymathy as "knowledge of various matters, drawn from all kinds of studies [...] ranging freely through all the fields of the disciplines, as far as the human mind, with unwearied industry, is able to pursue them". Von Wowern lists erudition, literature, philology, philomathy and polyhistory as synonyms. The related term, polyhistor, is an ancient term with similar meaning.Polymaths include the great thinkers of the Renaissance and the Enlightenment who excelled at several fields in science, technology, engineering, mathematics, and the arts. In the Italian Renaissance, the idea of the polymath was expressed by Leon Battista Alberti (1404–1472) in the statement that "a man can do all things if he will".Embodying a basic tenet of Renaissance humanism that humans are limitless in their capacity for development, the concept led to the notion that people should embrace all knowledge and develop their capacities as fully as possible. This is expressed in the term "Renaissance man", often applied to the gifted people of that age who sought to develop their abilities in all areas of accomplishment: intellectual, artistic, social and physical.

The term entered the lexicon in the 20th century and has now been applied to great thinkers living before and after the Renaissance.

Root beer

Root beer is a sweet North American soft drink traditionally made using the bark of the sassafras tree Sassafras albidum or the vine of Smilax ornata (sarsaparilla) as the primary flavor. Root beer may be alcoholic or non-alcoholic, most often non-alcoholic. It can be naturally free of caffeine or have caffeine added, and be carbonated or non-carbonated. It usually has a thick and foamy head when poured. Modern, commercially produced root beer is generally sweet, foamy, carbonated, non-alcoholic, and flavored using artificial sassafras flavoring. Sassafras root is still used to flavor traditional root beer, but since sassafras was banned by the U.S. Food and Drug Administration due to the carcinogenicity of its constituent safrole, most commercial recipes do not contain sassafras. Some commercial root beers do use a safrole-free sassafras extract. Major producers include A & W, Dr Pepper Snapple Group, Coca-Cola, Sprecher Brewery, Dad's Root Beer, Berghoff Beer, and Barq's.

Root mean square

In statistics and its applications, the root mean square (abbreviated RMS or rms) is defined as the square root of the mean square (the arithmetic mean of the squares of a set of numbers).

The RMS is also known as the quadratic mean and is a particular case of the generalized mean with exponent 2.

RMS can also be defined for a continuously varying function in terms of an integral of the squares of the instantaneous values during a cycle.

For alternating electric current, RMS is equal to the value of the direct current that would produce the same average power dissipation in a resistive load.In estimation theory, the root mean square error of an estimator is a measure of the imperfection of the fit of the estimator to the data.

Rooting (Android)

Rooting is the process of allowing users of smartphones, tablets and other devices running the Android mobile operating system to attain privileged control (known as root access) over various Android subsystems. As Android uses the Linux kernel, rooting an Android device gives similar access to administrative (superuser) permissions as on Linux or any other Unix-like operating system such as FreeBSD or macOS.

Rooting is often performed with the goal of overcoming limitations that carriers and hardware manufacturers put on some devices. Thus, rooting gives the ability (or permission) to alter or replace system applications and settings, run specialized applications ("apps") that require administrator-level permissions, or perform other operations that are otherwise inaccessible to a normal Android user. On Android, rooting can also facilitate the complete removal and replacement of the device's operating system, usually with a more recent release of its current operating system.

Root access is sometimes compared to jailbreaking devices running the Apple iOS operating system. However, these are different concepts: Jailbreaking is the bypass of several types of Apple prohibitions for the end user, including modifying the operating system (enforced by a "locked bootloader"), installing non-officially approved (not available on Google Play) applications via sideloading, and granting the user elevated administration-level privileges (rooting). Many vendors such as HTC, Sony, Asus and Google explicitly provide the ability to unlock devices, and even replace the operating system entirely. Similarly, the ability to sideload applications is typically permissible on Android devices without root permissions. Thus, it is primarily the third aspect of iOS jailbreaking (giving users administrative privileges) that most directly correlates to Android rooting.

Square root

In mathematics, a square root of a number a is a number y such that y2 = a; in other words, a number y whose square (the result of multiplying the number by itself, or y ⋅ y) is a. For example, 4 and −4 are square roots of 16 because 42 = (−4)2 = 16.

Every nonnegative real number a has a unique nonnegative square root, called the principal square root, which is denoted by √a, where √ is called the radical sign or radix. For example, the principal square root of 9 is 3, which is denoted by √9 = 3, because 32 = 3 · 3 = 9 and 3 is nonnegative. The term (or number) whose square root is being considered is known as the radicand. The radicand is the number or expression underneath the radical sign, in this example 9.

Every positive number a has two square roots: √a, which is positive, and −√a, which is negative. Together, these two roots are denoted as ±√a (see ± shorthand). Although the principal square root of a positive number is only one of its two square roots, the designation "the square root" is often used to refer to the principal square root. For positive a, the principal square root can also be written in exponent notation, as a1/2.Square roots of negative numbers can be discussed within the framework of complex numbers. More generally, square roots can be considered in any context in which a notion of "squaring" of some mathematical objects is defined (including algebras of matrices, endomorphism rings, etc.)

Square root of 2

The square root of 2, or the (1/2)th power of 2, written in mathematics as √2 or 2​1⁄2, is the positive algebraic number that, when multiplied by itself, gives the number 2. Technically, it is called the principal square root of 2, to distinguish it from the negative number with the same property.

Geometrically the square root of 2 is the length of a diagonal across a square with sides of one unit of length; this follows from the Pythagorean theorem. It was probably the first number known to be irrational.

As a good rational approximation for the square root of two, with a reasonable small denominator, the fraction 99/70 (≈ 1.4142857) is sometimes used.

The sequence A002193 in the OEIS gives the numerical value for the square root of two, truncated to 65 decimal places:


Tree (data structure)

In computer science, a tree is a widely used abstract data type (ADT)—or data structure implementing this ADT—that simulates a hierarchical tree structure, with a root value and subtrees of children with a parent node, represented as a set of linked nodes.

A tree data structure can be defined recursively as a collection of nodes (starting at a root node), where each node is a data structure consisting of a value, together with a list of references to nodes (the "children"), with the constraints that no reference is duplicated, and none points to the root.

Alternatively, a tree can be defined abstractly as a whole (globally) as an ordered tree, with a value assigned to each node. Both these perspectives are useful: while a tree can be analyzed mathematically as a whole, when actually represented as a data structure it is usually represented and worked with separately by node (rather than as a set of nodes and an adjacency list of edges between nodes, as one may represent a digraph, for instance). For example, looking at a tree as a whole, one can talk about "the parent node" of a given node, but in general as a data structure a given node only contains the list of its children, but does not contain a reference to its parent (if any).

Tree (graph theory)

In mathematics, and, more specifically, in graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path. Every acyclic connected graph is a tree, and vice versa. A forest is a disjoint union of trees, or equivalently an acyclic graph that is not necessarily connected.

The various kinds of data structures referred to as trees in computer science have underlying graphs that are trees in graph theory, although such data structures are generally rooted trees. A rooted tree may be directed, called a directed rooted tree, either making all its edges point away from the root—in which case it is called an arborescence, branching, or out-tree—or making all its edges point towards the root—in which case it is called an anti-arborescence or in-tree. A rooted tree itself has been defined by some authors as a directed graph.The term "tree" was coined in 1857 by the British mathematician Arthur Cayley.


Tubers are enlarged structures in some plant species used as storage organs for nutrients. They are used for the plant's perennation (survival of the winter or dry months), to provide energy and nutrients for regrowth during the next growing season, and as a means of asexual reproduction. Stem tubers form thickened rhizomes (underground stems) or stolons (horizontal connections between organisms). Common plant species with stem tubers include potato and yam. Some sources also treat modified lateral roots (root tubers) under the definition; these are encountered in sweet potato, cassava, and dahlia.

Plant groups
Plant morphology
Plant growth and habit
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