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from article Set theory
Sets of points on a plane.
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from article Set theory
Vertical projection of set X onto segment Y.
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from article Polygon
Triangle ABC with nine-point circle. Symbols are explained in text.
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from article Polygon
Regular pentagon, showing approximate construction without a protractor. Symbols are explained in text.
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from article Polygon
Polar triangles A, B, C and A′, B′, C′. The center of the sphere is at O. AQ and PB are 90° arcs, so angle C′ = arc PQ is the supplement of AB.
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from article Epicycloid
Diagram of an epicycloid.
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from article Camel
Bactrian camel (Camelus bactrianus). (Photo courtesy of Brent Huffman, Ultimate Ungulate Images)
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from article Plant communication
Hillsides in central California covered by hard chaparral composed almost entirely of chemise shrubs. Chemise (also spelled chamise) produces allelopathic chemicals that, through plant communication, inhibit the germination of seeds and the…
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from article Soil
Soil supports plant growth. A pumpkin seed in nutritious soil sprouts and comes to life. (Credit: Redmal/Getty Images)
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from article Soil
A soil profile showing horizons. This particular soil belongs to the Dothan series of soils, which are very deep, well drained soils that form in thick beds of unconsolidated, medium- to fine-textured marine sediments. (Credit: John A. Kelley,…
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from article Soil
Erosion is an important concern of soil management. The soil along the river bank has eroded significantly, causing riparian trees to fall. (Credit: Hans Engbers, Shutterstock)
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from article Dendrochronology
Ring patterns showing complacent and sensitive ring series. (a) Climate has minimal effect on ring widths when trees have ample moisture every year. (b) Maximum ring-width variations occur on sites where growth is limited by factors that vary from…
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from article Dendrochronology
Core being taken from a tree with an increment borer. (Courtesy of Laboratory of Tree-Ring Research, University of Arizona)
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from article Dendrochronology
Chronology building. Chronologies are extended backward in time by matching patterns of wood samples whose ages overlap.
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from article Dendrochronology
Skeleton plot (top) from an idealized tree-ring sequence in a specimen (bottom). Ring widths are represented by vertical lines in inverse proportion; that is, tall lines represent narrow rings. An exceptionally wide ring is designated by the letter…
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from article Dendrochronology
Bristlecone pines, which attain ages of more than 4000 years, form the basis for the second longest chronology yet developed. (Courtesy of Laboratory of Tree-Ring Research, University of Arizona)
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from article Paleoindian
Location of some important North American Paleoindian sites during the late-Pleistocene Ice Age.
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from article Sleep-dependent memory processing
The sleep cycle, memory systems, and memory stages. (a) The human sleep cycle. Across the night, rapid eye movement (REM) sleep and non-REM (NREM) sleep cycle every 90 minutes in an ultradian manner (that is, occurring in cycles that are repeated…
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from article Sleep-dependent memory processing
Sleep-dependent motor skill learning. (a) Wake first. After morning training (10 a.m., clear bar), subjects showed no significant change in performance when tested after 12 hours of wake time (10 p.m., clear bar). However, when tested again…
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from article Sleep-dependent memory processing
Sleep-dependent integration of human relational memory. (a) Delayed inference (associative) memory performance (% correct) in a relational memory task following different offline delays. Immediate testing after just a 20-min offline delay…
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from article Territoriality
The tiger (Panthera tigris) is highly territorial in its behavior. (Credit: Safique Hazarika Photography/Getty Images)
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from article Fossil primates
Representatives of living primate families. (Copyright © McGraw-Hill Education)
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from article Fossil primates
Carpolestes simpsoni, a 55.5-million-year-old plesiadapiform from Wyoming: (a) skeleton as recovered, laid out in approximate anatomical position; (b) reconstruction in life stance on a tree branch; elements in dark gray are known; (c) external…
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from article Fossil primates
Cranium of the omomyoid tarsiiform Teilhardina asiatica, from deposits dated approximately 55 MYA in China: (a) dorsal (top) view as found; (b) left lateral reconstruction. (Credit: Xijun Ni)
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from article Fossil primates
Anjohibe (Madagascar) specimen of Palaeopropithecus ingens (an extinct lemur), mounted in a probable habitat posture. (Credit: American Geological Institute)
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from article Fossil primates
Partly reconstructed skeleton (casts) of Paracolobus chemeroni, a 3.2-million-year-old colobine monkey from Kenya, on exhibit at the American Museum of Natural History in New York. (Credit: Eric Delson)
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from article Fossil primates
Reconstructed skeleton of Proconsul heseloni, an early hominoid (23–14 MYA) from East Africa. Known parts are shaded. (Credit: R. L. Ciochon and R. S. Corruccini)
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from article Ecological competition
The competitive exclusion principle can be prevented through resource partitioning and species coexistence. In this illustration, each warbler species prefers to feed at a different height and portion of the tree, thus reducing competition.…
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from article Hunger
Principles of appetite regulation by gut–brain peptides. Tissues and organs, including the pancreas, stomach, small intestine, adipose tissue, and large intestine, are sources of peptides that stimulate or inhibit appetite-regulating neurons in the…
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from article Biosphere
All environments capable of sustaining life above, on, and beneath the Earth's surface, as well as in the oceans, are contained in the biosphere. (Credit: National Aeronautics and Space Administration)
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from article Biosphere
The upper and lower limits of the biosphere are not sharply defined. However, most of the biosphere lies within the zone that is reached by sunlight and where liquid water exists. The mountains shown in this photograph are located in Torres del…
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from article Predator-prey interactions
A predatory panther chameleon (Furcifer pardalis) is preying upon a cricket. (Credit: Cathy Keifer/Shutterstock)
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from article Predator-prey interactions
Predator-prey interactions play important roles in explaining the population dynamics of many species. In this photograph, a cheetah (Acinonyx jubatus) is hunting a springbok (Antidorcas marsupialis) in Namibia. (Credit: Elana Erasmus/Shutterstock)
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from article Predator-prey interactions
Snowshoe hare populations (solid blue circles) and lynx populations (white squares) inferred from the numbers of pelts sold to the Hudson's Bay Company. (Credit: Based on data compiled by D. A. MacLuclich; copyright © McGraw-Hill Education)
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from article Food web
The trophic levels of a food chain, which is one particular route through a food web, are often separated into primary producers, primary consumers (herbivores), and secondary consumers. (Copyright © McGraw-Hill Education)
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from article Food web
In a food web, the energy that plants capture from the sun during photosynthesis may end up in the tissues of a hawk. It gets there via a sparrow that the hawk has eaten, the insects that were eaten by the sparrow, and the plants on which the…
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from article Difference equation
Numerical solution of Eq. (32) for a = 0.05, b = 0.1, c = 0.01, and a step input. The solution uses the state-variable representation of Eq. (33) and the difference-equation approximation of Eq. (36) with h = 0.1.
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from article Cycloid
Diagram of cycloid; symbols explained in text.
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from article Field theory (mathematics)
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from article Field theory (mathematics)
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from article Speech perception
The perception of speech (as well as the production of speech) involves interactive processes occurring in various regions of the brain. Researchers also have noted the important contribution that vision makes to normal speech perception. (Copyright…
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from article Speech perception
An auditory spectrogram of the word "telephone." (a) The vertical striations in the bands represent amplitude modulation at the frequency of the voice pitch. Such striations are absent from the initial noise portion corresponding to the voiceless…
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from article Information theory (biology)
Human information processing. The estimates of channel capacity are based on the number of rods in the retina of the eye and the number of hair cells in the inner ear's organ of Corti.
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from article Information theory (biology)
Flow diagram of communication.
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from article Information theory (biology)
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from article Information theory (biology)
Coupling diagram of communication.
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from article Biomass
Wood materials are common sources of biomass. They can be burned directly for energy or processed in industrial facilities to produce renewable biofuels. (Credit: alffoto/Getty Images)
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from article Biomass
Carbon cycle, showing conversion of solar energy to fuel and electricity. (Copyright © McGraw-Hill Education)
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from article Biomass
Methods of converting biomass to energy, fuels, and chemicals. (Copyright © McGraw-Hill Education)
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from article Invasive forest species
The emerald ash borer (Agrilus planipennis) is a destructive invasive forest species. Native to northeastern Asia, this wood-boring beetle has devastated large areas of forests in North America and Europe. (Credit: Benjamin Smith)
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from article Invasive forest species
Perennial vine legume kudzu (Pueraria montana) growing in California. (Copyright © California Department of Food and Agriculture)
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from article Surface (geometry)
Part of a dihedron (the rest has been torn away), showing dihedral angle.
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from article Surface (geometry)
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from article Surface (geometry)
Some quadric surfaces, with parameters a, b, and c. (a) Ellipsoid; 0 < c < b < a. (b) Hyperboloid of one sheet; 0 < a < b < c. (c) Elliptic paraboloid; 0 < a < b and c > 0. (d) Hyperboloid of two sheets; 0 < a < b < c. (e) Hyperbolic paraboloid; c >…
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from article Surface (geometry)
Surface of revolution. The generating curve (in the yz plane) is f(y,z) = 0. The axis of revolution is the z axis.
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from article Surface (geometry)
Sphere, with a zone and a lune.
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from article Surface (geometry)
Catenoid. The axis of revolution is the y axis.
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from article Interpolation
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from article Interpolation
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from article Interpolation
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from article Autopilot
Basic elements of an autopilot system.
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from article Autopilot
Typical longitudinal autopilot control loop.
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from article Autopilot
Typical directional autopilot control loop.
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from article Fossil apes
Reconstructions and partial reconstructions of the craniums of fossil apes: (a) Proconsul, (b) Afropithecus, (c) Oreopithecus, (d) Ouranopithecus, (e) Sivapithecus, and (f) Ankarapithecus.
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from article Fossil apes
Cladogram of the evolutionary relationships of the key fossil and living apes. Broken lines indicate uncertain relationships.
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from article Plant
The kingdom Plantae contains a tremendous diversity of plants. The plants seen in the photograph are drought-tolerant varieties native to California and the Mediterranean region. (Credit: David Madison/Getty Images)
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from article Problem solving (psychology)
Composite view of a colorized magnetic resonance imaging (MRI) scan of a human brain blended with a cross-section illustration of a human head. Cognitive psychology attempts to understand the integral mental processes of the human brain involved in…
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from article Problem solving (psychology)
The game of chess involves many aspects of problem solving. In chess playing, a solution consists of an attempt to convert an initial state of a task (for example, a chessboard before the first move is made) into a final or goal state (checkmate)…
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from article Agroecosystem
A group of pigs at a pig breeding farm. (Credit: Shutterstock / DN1988)
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from article Agroecosystem
Glysophate-resistant Palmer pigweed growing uncontrolled in Roundup Ready soy beans. (Credit: Bill Barksdale / Design Pics/Getty Images)
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from article Population ecology
Relationship between prey and predator populations. The abundance curve (population density versus time) for the predator lags behind that of the prey. (Copyright © McGraw Hill)
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from article Population ecology
Carrying capacity is a measure of the largest number of individuals that can be sustained in a given space. The population reaches a stable equilibrium phase when the carrying capacity is approximately maintained. (Copyright © McGraw Hill)
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from article Graph theory
Königsberg bridge problem. (a) The seven bridges of Königsberg. (b) Corresponding graph.
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from article Graph theory
Two isomorphic graphs.
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from article Graph theory
Two graphs for which either a 120° rotation or a vertical reflection is an automorphism.
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from article Graph theory
Homeomorphic but nonisomorphic graphs.
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from article Graph theory
Plane map requiring four colors.
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from article Graph theory
Map on a torus (doughnut) that requires seven colors. To form the torus, paste opposite sides of the rectangle together.
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from article Graph theory
Prototypes of all nonplanar graphs.
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from article Graph theory
A digraph and its adjacency matrix.
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from article Graph theory
A tournament.
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from article Graph theory
The two isomers of a saturated hydrocarbon.
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from article Graph theory
Matrix-tree theorem. (a) Graph G. (b) Corresponding matrix A. (c) Spanning trees of G.
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from article Recursive function
Turing machine scanning a single block on its tape.
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from article Guild
Guilds of granivorous rodents in three deserts in the southwest United States. Mean weight (in grams) of each species is plotted on the body mass axis. The body mass scale is logarithmic, so that equal spacing shows equal ratios. (After M. A. Bowers…
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from article Laplace's differential equation
Circular disk D of radius a.
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from article Dialectical behavior therapy
Dialectical behavior therapy (DBT) is a psychotherapy that focuses on increasing skills to process emotions, solve problems, understand the functions of behaviors, and change contingency patterns. Four sets of skills are arranged around the…
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from article Polar navigation
Polar stereographic graticule with polar grid.
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from article Polar navigation
An astrocompass.
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from article Polar navigation
Ship negotiating pack ice.
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from article Solid (geometry)
Cylindrical solid. The height of the solid is h, and the area of the bases is A.
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from article Solid (geometry)
Conical solid. The height of the solid is h, and the area of the base is A.
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from article Solid (geometry)
Pseudosphere formed by revolving a tractrix about the y axis.
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from article Biodegradation
Biodegradation of the compounds contained in oil spills can be accomplished by microorganisms. The use of microorganisms to remediate the environment of contaminants (for example, petroleum) is referred to as bioremediation. (Credit: Tasha…
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from article Instinctive behavior
One obvious releasing stimulus for instinctive predatory behavior in the cat is a mouse. If the neural system for predation is in an active state, the prey will elicit the typical attack response. (Credit: Jasper White/Image Source)
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from article Soil fertility
Close-up view of corn germinating in fertile (nutrient-rich) soil. Proper soil fertility is necessary to support the germination and growth of plants. (Credit: Petro Perutskyi, Shutterstock)
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from article Soil fertility
For the optimal growth of plant tissues, essential nutrients need to be absorbed from the soil. The graph shows plant growth in response to changes in tissue nutrient concentration. (Credit: Based on an original graph by E. Epstein and A. J. Bloom)
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from article Algebra
Algebraic equations involve variables; in this case, a and b, which stand for unknown values. (Credit: Shutterstock / Silvio Cuccu)
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from article Algebra
Representations of number systems. (a) Of real numbers on a number line. (b) Of complex numbers on a two-dimensional plane.
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from article Algebra
Representation of relations by graphs. (a) Graphic depiction of an ordered pair (a, b) given by an equation. (b) Graph of the function f(x) = x2 + 3.
