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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 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 Science
Italian physicist and astronomer Galileo Galilei (1564–1643) founded the modern scientific method of deducing laws to explain the results of observation and experiment. (Credit: Getty Images)
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from article Kutorginata
Kutorgina, showing (a) exterior of pedicle (ventral) valve; (b) lateral view of shell; (c) exterior of brachial (dorsal) valve. (After C. D. Walcott, Cambrian Brachiopoda, USGS Monogr., vol. 51, 1912)
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from article Fossil seeds and fruits
Early Tertiary fruits and seeds which were found in the Brandon lignite of Vermont. (a) Endocarps of Symplocos. (b) Seeds of grape (Vitis). (c) Seeds of Rubus. (d) Endocarp of extinct species of Nyssa. (e) Seeds of fossil genus of family Rutaceae,…
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from article Pinales
Leaf, branch, and cone characteristics of conifers. (a) Branch of pine with leaves and ovulate cones. (b) Ovulate cone of spruce cut longitudinally to show scales with ovules. (c) Detail of one scale with two ovules. (Copyright © McGraw-Hill…
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from article Pinales
Fertile dwarf shoots of a cordaite and select fossil conifers, representing stages in cone scale evolution. A direct phylogenetic series is not implied. (a) In Cordaites, the ovules were borne terminally on the megasporophylls. (b) Emporia. (c) The…
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from article Selaginellales
Characteristic features of a typical heterophyllous selaginellalean of the Stachygynandrum type. (After T. R. Webster, Developmental problems in Selaginella in an evolutionary context, Ann. Mo. Bot. Gard., 79:633–647, 1992)
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from article Carboniferous
Carboniferous, the fifth period of the Paleozoic Era.
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from article Carboniferous
Development of stratigraphic nomenclature for the Carboniferous.
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from article Carboniferous
Curves outlining the fluctuations of sea level during the Carboniferous. The Mississippian sea-level curve is typical of times when glaciation was not a major factor in controlling sea levels, and the Pennsylvanian sea-level curve is characteristic…
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from article Carboniferous
Paleogeography of the Carboniferous. (a) Early Carboniferous (Mississippian) Tournaisian and Visean epochs, with a major east-west equatorial seaway between Euramerica and Gondwana. (b) Late Carboniferous (Pennsylvanian) Moscovian (or Desmoinesian)…
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from article Carboniferous
Typical shelf sedimentary patterns in Upper Carboniferous depositional sequences. The broken line represents the condensed section that forms during maximum sea-level highstands when sedimentation rates are low. The prominent unconformities at the…
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from article Asteroidea
A five-armed sea star (genus Fromia) resting on coral in the waters surrounding the Maldive Islands. (Credit: Ian Cartwright/Getty Images)
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from article Asteroidea
A representative asteroid, Astrostole scabra. (Copyright © McGraw-Hill Education)
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from article Asteroidea
The Pacific blue sea star (Linckia laevigata) belongs to the asteroid order Valvatida. This sea star is common in the tropical waters of the Indo-Pacific. (Credit: Comstock Images/Getty Images)
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from article Asteroidea
A large sun sea star (Solaster stimpsoni) in the intertidal-zone waters of Kodiak Island, Alaska. (Credit: Mandy Lindeberg/National Oceanic and Atmospheric Administration)
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from article Asteroidea
Transverse section through an asteroid arm. (Copyright © McGraw-Hill Education)
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from article Asteroidea
Anatomy of a sea star, Diplodontias robustus, as viewed from the aboral surface. (Copyright © McGraw-Hill Education)
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from article Burgess Shale
Marrella splendens, a characteristic Burgess Shale arthropod. The head shield bears two prominent pairs of spinose extensions; also visible are various appendages that include walking legs and gills. The prominent dark areas appear to represent…
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from article Burgess Shale
Cathaymyrus diadexus, a primitive chordate from the Chengjiang assemblage of China. The body is eellike, and at the anterior there are a pharynx and gill slits. (Copyright © Simon Conway Morris)
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from article Burgess Shale
An articulated halkieriid, Halkieria evangelista, from the Sirius Passet fauna, North Greenland. The body was coated with platelike sclerites, and at either end carried a large shell. (Copyright © Simon Conway Morris)
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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 Platyasterida
Ventral view of an arm and a portion of the disk of Platanaster ordovicus. Note lateral alignment of the arm plates. (After W. K. Spencer and C. W. Wright, Asterozoans, in R. C. Moore, Treatise on Invertebrate Paleontology, Pt. U, Echinodermata 3,…
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from article Rugosa
Rugose corals. (a) Aulacophyllum sp. of horn coral showing the major external features of a solitary coral skeleton; septa pinnately arranged about the cardinal fossula. Devonian, North America, ×0.75. [Most rugose corals need to be studied in thin…
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from article Rugosa
Rugose coral skeletons. (a) Palaeocyclus porpita, discoidal corallite, calical view with platelike epitheca beneath, cardinal septum shortened. Silurian, Sweden, ×2. (b) Caninia sp., typical horn coral in growth orientation with septa visible in the…
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from article Rugosa
Rugose coral skeletons. (a) Siphonphyllia gigantea, solitary cylindrical corallites prone on bedding plane; individual bottom-right showing sharp change of growth direction. Carboniferous, Ireland; width of photo, 1 m. (b) Arachnophyllum pentagonum,…
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from article Cycloid
Diagram of cycloid; symbols explained in text.
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from article Hyracoidea
Cape hyrax (Procavia capensis). (Photo by Lloyd Glenn Ingles; copyright © California Academy of Sciences)
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from article Bivalvia
Freshwater mussels (subclass Paleoheterodonta, class Bivalvia) in the Missouri River. (Credit: U.S. Fish and Wildlife Service)
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from article Bivalvia
Red shell of a spiny oyster (genus Spondylus, subclass Pteriomorphia, class Bivalvia). (Credit: Pablo Hidalgo/123RF)
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from article Bivalvia
Bivalve anatomy as represented by the quahog clam (Mercenaria mercenaria). (Copyright © McGraw-Hill Education)
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from article Field theory (mathematics)
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from article Field theory (mathematics)
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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 Cetacea
Dusky dolphins (Lagenorhynchus obscurus) in the coastal waters of New Zealand. (Credit: Mridula Srinivasan/Assessment and Monitoring Division, Office of Science and Technology, National Marine Fisheries Service, National Oceanic and Atmospheric…
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from article Cetacea
Killer whale (Orcinus orca) in Monterey Bay, California. (Credit: Tory Kallman/Getty Images)
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from article Cetacea
A humpback whale opens its mouth wide to collect prey, and then filters food from the water using its baleen. (Credit: John Tunney/Shutterstock)
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from article Cetacea
Sperm whales (Physeter macrocephalus). (Credit: Gabriel Barathieu)
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from article Cetacea
Skeletal reconstruction of Ambulocetus natans. (Credit: J. G. M. Thewissen)
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from article Cetacea
Cetacean fossils. (a) Left upper premolar. (b) Skull of Dorudon atrox (alternatively Prozeuglodon stromeri) from the early Oligocene of Egypt. (c) Skull of Delphinodon dividum from the middle Miocene of Maryland. (Copyright © McGraw-Hill Education)
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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 Conodont
Conodont elements: (a, b) coniform elements, (c, d) ramiform elements, (e, f) pectiniform blade elements, (g, h) pectiniform platform elements, (i) beddingplane assemblage.
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from article Conodont
The first specimen of the conodont animal discovered in Lower Carboniferous rocks in Edinburgh. (a) Photograph of specimen. (b) Outline of the specimen for comparison. (From D. E. G. Briggs, E. N. K. Clarkson and R. J. Aldridge, The conodont animal,…
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from article Conodont
Head region of the conodont animal, showing the conodont elements on the side of the slab opposing that illustrated in Fig. 2. (From D. E. G Briggs, E. N. K Clarkson, and R. J. Aldridge, The conodont animal, Lethaia, 16:1–14, 1983)
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from article Plesiosauria
Skeleton of the plesiosauroid Cryptocleidus, about 10 ft (3 m) long.
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from article Time-averaging (paleontology)
Estimates of temporal mixing for modern and fossil assemblages from terrestrial and marine depositional systems. [From Fig. 3 of A. K. Behrensmeyer, S. M. Kidwell, and R. A. Gastaldo, Taphonomy and paleobiology, Paleobiology, 26:103–147, 2000, with…
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from article Sphenophyllales
Reconstruction of Sphenophyllum cuneifolium, showing whorled leaves and two cones. (After G. M. Smith, Cryptogamic Botany, vol. 2, 2d ed., McGraw-Hill, 1955)
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from article Petrified forests
Tall petrified tree trunks on Specimen Ridge in Yellowstone National Park, Wyoming. (Credit: William W. Dunmire/National Park Service)
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from article Petrified forests
Petrified wood log tumble in Petrified Forest National Park, Arizona. (Credit: T. Scott Williams/National Park Service)
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from article Petrified forests
Map showing the locations of the principal petrified forests listed in the stratigraphic chart of Fig. 4 and mentioned in the text. Note that the location of the Fremouw forest in east Antarctica is not visible on this map projection. (Copyright ©…
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from article Petrified forests
Chart showing the stratigraphic positions of the known principal petrified forests. The numbers in parentheses following the petrified forest names correlate with the numbers showing the forest locations on the map of Fig. 3. (Copyright © McGraw…
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from article Pentamerida
Interior views of pentamerides. (a) Porambonites, dorsal interior. (b) Camerella, ventral interior. (c) Interior of the posterior end of Parastrophina with dorsal valve above and ventral valve below.
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from article Pentamerida
Kirkidium, of the Silurian, (a) lateral and (b) dorsal views.
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from article Dipnoi
Lateral views of lungfish skulls: (a) African lungfish, Protopterus aethiopicus; (b) Australian lungfish, Neoceratodus forsteri.
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from article Dipnoi
Australian lungfish (Neoceratodus forsteri). (Photo copyright © Johnny Jensen)
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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 Holostei
Cuban gar (Atractosteus tristoechus). (Photo by Milan Kořínek)
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from article Recursive function
Turing machine scanning a single block on its tape.
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from article Laplace's differential equation
Circular disk D of radius a.
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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 Gastropoda
Typical turbinate shell of gastropods. (a) Longitudinal section ground through the shell of a specimen of Conus purius to reveal the central columella and spiral of whorls expanding to the aperture. (b) Diagram of the shell to show the relationship…
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from article Gastropoda
Further evolution of the mantle cavity in gastropods. The mantle cavity and pallial complex is shown (a) in dorsal view and (b) in cross section for an asymmetric snail with a single aspidobranch gill, and (c, d) for an asymmetric snail with a…
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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.
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from article Algebra
Graphs of the relations described by the equations (a) y = 2x2 − 4x + 5 and (b) y2 = x − 1. The vertical-line test shows that the first relation is a function while the second is not.
