How To Use Geometry In A Sentence
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In addition to the NOx adsorber and the DPF, the 6. 7-liter turbodiesel engine includes a cooled exhaust gas recirculation (EGR) system and high-flow, electronically controlled Variable Geometry Turbocharger (VGT ™); an oxidation catalyst within the exhaust system; and a new closed crankcase ventilation system that eliminates crankcase fumes and oil carryover.
Autoblog
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Related, but not directly, I have spent much time getting to know fractals, 4d geometry, and other ‘strange’ mathematical phenomena.
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Finally, we indicate the source of such inconsistent analysis, namely, an effect due to the geometry of tumors, and how to fix it.
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It seemed to him that the ground was prearranged into a form of complex geometry.
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The engraving shows that Geometry / Melancholy has not succeeded in fashioning a regular dodecahedron.
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The Karmarkar method starts in the inside of the polytope, then uses a technique called projective geometry to warp the whole structure, again and again, in effect changing the shape of the polytope, over and over, until the best solution is achieved.
Economic Principals
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In the first place, chemical solutions can conform to the geometry of the sample vessel or object being irradiated.
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An operator can input the parameters that define the geometry of the valve seat profile.
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Much of classical astrology developed as a result of the Hellenistic perspective towards numerology and geometry.
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He was the first to identify the group of four canonical sciences (logistic [arithmetic], geometry, astronomy and music), which would become known as the quadrivium in the middle ages.
Archytas
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It could only do some partial unifications, such as the geometry of conics and the theory of equations.
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Slowly Caroline turned more and more towards helping William with his astronomical activities while he continued to teach her algebra, geometry and trigonometry.
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Saccheri then studied the hypothesis of the acute angle and derived many theorems of non-Euclidean geometry without realising what he was doing.
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It is, rather, a handbook for philosophy students, written to illustrate how arithmetic, geometry, stereometry, music, and astronomy are interrelated.
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Its massive sundials and other structures are a geometry of red sandstone inlaid with dazzling white marble, more like works of modern art than scientific instruments.
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The difficulties of the site - its geometry, its western orientation, an adjacent future road easement and its flood prone nature - were significant determinants in the ensuing design.
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The real choice is between becoming a fully fledged United States of Europe, or remaining little more than a modern-day Holy Roman Empire, a gimcrack hodgepodge of "variable geometry" that will sooner or later fall apart.
The End of the Euro
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Vases of every shape and design, minimalist masks that look like faces and vice-versa, and numerous experiments with geometry confront the visitor.
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(1997, 2006, 2008) defends an empiricist and non-realist form of structuralism about science, motivated by an illuminating reconstruction of the origins of structuralism in the debate about the epistemology of physical geometry in the nineteenth century, and more generally in the progressive mathematisation of science.
Structural Realism
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The Greeks invented the science of geometry with practical applications in architecture in mind.
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Omar Khayyam, known chiefly in Europe as a poet, combined trigonometry and approximation theory to solve algebraic equations using geometry.
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This work contains fundamental ideas of projective geometry such as the cross-ratio, perspective, involution and the circular points at infinity.
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The book contained the elements of geometry and algebra in addition to the calculus.
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Because of the clarity and care with which his elementary texts on analytic geometry and trigonometry were written they are still in demand.
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Yet it can hardly be called nonmathematical, although little more than some simple geometry and arithmetic is needed to understand it.
Dictionary of the History of Ideas
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We take the geometry method to derive the inverse kinematics and the center of pressure (COP) of the biped robot.
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His most important mathematical contribution is the application of geometry to optics.
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His great love within mathematics was geometry, and this turned out to be his lifelong field.
Times, Sunday Times
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Reye's early interest in mathematical physics and meteorology turned to an interest in geometry even while he held the lectureship in mathematical physics at Zurich.
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The Egyptian hieroglyph for ‘city’ was a circle surrounding a cross; but squares and grids were always the more favoured geometry of utopian planners.
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However he also worked on differential equations, matrices and other topics in algebra, continued fractions, geometry and number theory.
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He wrote several books on arithmetic, algebra, geometry and astronomy.
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Hermite had a kind of positive hatred of geometry and once curiously reproached me with having made a geometrical memoir.
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He wrote several books on arithmetic, algebra, geometry and astronomy.
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Lexell made major contributions to spherical geometry and trigonometry.
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The scholastic records of this college student with callosal agenesis were fair to good for courses that involved language and verbal facility, but contrastingly poor for subjects such as geometry and geography that involved spatial and related nonverbal faculties which we now commonly associate with the right hemisphere.
Roger W. Sperry - Nobel Lecture
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This results in not just noncommutative geometry, but nonassociative structure as well.
Can a Really, Really Fast Spacecraft Turn Into A Black Hole? | Universe Today
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When, later, in stereometry [solid geometry], an appeal was made to my imagination, it went a bit better, but in school I never excelled in that subject.
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Geometry Blaster is from the Davidson company, a pioneer in educational software.
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Some of the early investigators of chaos were the American physicist Mitchell Feigenbaum; the Polish-born mathematician and inventor of fractals see fractal geometry Benoit Mandelbrot; the American mathematician James Yorke, who popularized the term chaos; and the American meteorologist Edward Lorenz.
Exponential Growth in Physical Systems #2 « Climate Audit
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The theorem holds in spherical and elliptic geometry.
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The geometry on this racquet aids the beginner by increasing stability and power.
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Boethius seems to have been the first to use the term quadrivium, joining music with the mathematical arts of arithmetic, geometry, and astronomy.
MUSICAL GENIUS
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Inspired by the fact that it was possible to hide one extra dimension by wrapping it up in a circle, generally the extra 6 or 7 dimensions are thought to be “compactified” into a very small compact geometry like a sphere or a torus.
Making Extra Dimensions Disappear
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This wasn't any alien habitat, where even geometry might be twisted out of shape.
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Using sunlight and starlight as its source, the work manifests experiences of primal solar color, and star geometry in sculptural form.
2004 July « Mudpuddle
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This ‘index theorem’ had antecedents in algebraic geometry and led to important new links between differential geometry, topology and analysis.
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After the modeling section is complete we will switch gears and get into UV layouts, which is taking all the modeled geometry and converting it to a flat pintable map to apply textures on them in a painting program.
News
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His research interests include topology, algebraic geometry, and Lie theory.
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This occurs in the case of problems related to one another as subordinate and superior, as when optical problems are subordinated to geometry, mechanical problems to stereometry, harmonic problems to arithmetic, the data of observation to astronomy.
Posterior Analytics
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There wasn't so much as a geometry book in sight as the new timetable began with classes ranging from meditation and massage to yoga and tai chi.
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geometry is the mathematical science of shape
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His texts include books on algebra, mechanics, geometry and analysis.
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This paper presents a new method for an estimation of the axis of rotation based on line element geometry and kine-matic equation.
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Would the present obsession with fractal geometry have come about anyway as part of the ever changing taste of architectural stylists, or is it an inevitable result of computer power?
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We've recently conducted several pilot studies in the Marcellus and other North American shales that have demonstrated how we can help our clients determine reservoir rock properties, such as brittleness and natural fracture networks, and help predict the geometry of hydraulically induced fractures, both of which are critical to well planning, stimulation and completion.
ION Announces Multi-Client Seismic Survey in Marcellus Shale - Yahoo! Finance
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Pre-Christian sacred geometry was incorporated into church architecture.
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Bernhard Riemann pioneered elliptic geometry
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But taking that route causes problems later on, because the intermediate course fails to cover much basic algebra and geometry, of which the A-level course assumes knowledge.
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Of course, almanacs for the elite cannot be prepared without numbers and geometry, but the architecture as a whole can be disclosed by much simpler arguments; grade school experience suffices.
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Heller's current work focuses on noncommutative geometry and groupoid theory in mathematics which attempts to remove the problem of an initial cosmological singularity at the origin of the universe.
Assessing Causality
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The mathematical ballistics of 1918 was neither as refined as axiomatic geometry nor as theoretical as algebraic topology.
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It is devoted mainly to arithmetic and algebra, with just a few problems on geometry and mensuration.
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Expand Work Geometry in the Derived Part dialog box, and exclude all work features other than Work Plane-BOTT of Frame.
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“Emma,” Nima said, “the answer to your conic geometry question—which is my specialty—is ninety times pi.”
Times Squared
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Benoit Mandelbrot pioneered fractal geometry
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Wisdom is then knowledge of these two forms, which are studied by the four sciences, which will later be known as the quadrivium: arithmetic, music, geometry and astronomy.
Pythagoreanism
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His interest in mathematics was stimulated during his school years in Izmir by a teacher who encouraged him to solve problems in euclidean geometry.
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Euclidean geometry, Fibonacci numbers, the digits of pi, the notion of algorithms, concepts of infinity, fractals, and other ideas furnished the mathematical underpinnings.
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he mastered only the rudiments of geometry
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The binding geometry determined by interaction of the residues and bases in recognition area is indicated in the stereochemical chart.
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Tarski made important contributions in many areas of mathematics: set theory, measure theory, topology, geometry, classical and universal algebra, algebraic logic, various branches of formal logic and metamathematics.
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At the Guggenheim there will be one singer, whose voice will be completely distorted by the nautiloid curves of the museum and a PA system, so I'm going to have to break down the visual vocabulary of abstraction and directly connect it to the forces and geometry described in the Randall/Sundrum model.
Matthew Ritchie: A Perilous Intellectual High Wire Act
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The breakthrough that set the LuciaStove apart from similar gasifer stoves was Mulcahy's patented design which uses venturi holes to create negative pressure while a flame cap based on Fibonacci spiral geometry prevents oxygen from entering the pyrolysis chamber.
Kelpie Wilson: WorldStove: Transforming Haiti and the World
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I'm not pressing for new names for time-worn concepts, I'm objecting to the way people treat English grammar as if it were a frozen collection of eternal truths like Pythagorean geometry.
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It further provided that our civil rights have no dependance on our religious opinions, any more that our opinions in physics of geometry; and it concluded that no man shall be compelled to frequent or support any religious worship, place, or ministry whasoever, nor shall be enforced, restrained, molested, or burthened in his body or goods, nor shall otherwise suffer, on account of his religious opinions or belief.
Denis Lacorne: Rick Perry's War On The Founding Fathers
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The triangle is a kind of atomic unit in geometry.
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He established a geometry and topology based on group theory without the concept of a limit.
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The finite element mesh subdivides the geometry into elements, upon which are found nodes.
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Courses of instruction listed in the 1846 Catalogue include: Spelling, grammar, arithmetic, geography, uranography, composition, botany, physiology, algebra, natural philosophy, metal and moral science, rhetoric, chemistry, geometry, criticism, history, logic, trigonometry, astronomy, mineralogy, Butler's analogy, and evidences of Christianity.
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Paris and I suffered through Geometry together, splitting up afterwards so that she could go to art and I could go to orchestra.
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But the ludic presence of humor also inflects the choice of procedures and devices which hail us with their math or italic geometry.
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He clearly was trying to argue against the notions current at the time on using algebra to study geometry.
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His interests are in discrete differential geometry and mathematical visualization.
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The - 800's fuselage is shortened by 10 frames (six forward and four aft), which McConnell says requires changes to the geometry of section 13/14 (forward), section 16/18 (rear) and the upper shell of section 15 (centre fuselage).
HEADLINES
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Although the result is a non-standard account of geometry as an inexact science, Hume thinks that he thereby preserves reason from otherwise irresolvable antinomies.
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Hence, although we fix the vessel under distension, once the load is removed, the elastin will recoil and consequently have a tortuous geometry.
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It has proved to be the computational method of choice for symbolic manipulation in algebraic geometry, differential equations, and combinatorics.
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Comprises topics in algebra, geometry, trigonometry and elementary calculus at higher level.
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His buildings are radical, from the geometry of their floor plans to the perforated walls that filter light into the interiors.
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There Alcuin taught the seven sciences of the "trivium" and "quadrivium", i.e. grammar, rhetoric, and logic, arithmetic, music, geometry, and astronomy.
The Catholic Encyclopedia, Volume 2: Assizes-Browne
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Geometry dominates, for the axial symmetry of the Barry building is extended eastwards.
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His research focuses on the interplay between fractal geometry and stochastic processes.
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It should be remembered that in his era there was little thought or knowledge of fractal geometry, curved space or different degrees of infinity.
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'What with their courses of perspective, of descriptive geometry, of stereotomy, of building, and of the history of art -- ah! upon my word, they do make one blacken paper with notes.
His Masterpiece
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SE of Lang San the fault zone broadens out to form a strike-slip duplex geometry.
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This geometry should be taken into consideration when specifying a lens or telescope to image onto the slit, to prevent vignetting.
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While pursuing his theological studies he prepared a doctoral thesis on geometry.
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Max Einstein in the 12 - year - old , gave him a Spilker the plane geometry textbook.
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He began to study the geometry of infinitesimals and wrote to Oldenburg at the Royal Society in 1674.
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Each level of expression contributed to the next, and over the course of millennia we created mathematical theory, from basic arithmetic to algebra, from calculus to fractal geometry.
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Her latest work, Geometry of Quiet, which received its North American premiere, shows Brown in a mood of restrained, judiciously measured eloquence.
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Curvature is a measure of the local geometry of the surface, while the strain rates measure its relative rate of expansion.
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His research interests include topology, algebraic geometry, and Lie theory.
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We conclude from the Papyrus Rhind (say 1700 B. C.) and other documents that Egyptian geometry consisted mainly of practical rules for measuring, with more or less accuracy, (1) such areas as squares, triangles, trapezia, and circles, (2) the solid content of measures of corn, &c., of different shapes.
The Legacy of Greece Essays By: Gilbert Murray, W. R. Inge, J. Burnet, Sir T. L. Heath, D'arcy W. Thompson, Charles Singer, R. W. Livingston, A. Toynbee, A. E. Zimmern, Percy Gardner, Sir Reginald Blomfield
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To Archimedes came a way to calculate density and volume; to Descartes, the idea of coordinate geometry; and to Newton, the law of universal gravity.
A Wandering Mind Heads Straight Toward Insight
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Its prime role is to measure the track geometry to locate faults such as spreading and twisting.
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In addition to his work on geometry, Bolyai developed a rigorous geometric concept of complex numbers as ordered pairs of real numbers.
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He compared grammar with geometry because they both abstracted from concrete instances to provide laws and rules for individual cases.
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● Piron's result: from elementary questions recover the geometry of the Hilbert space (over the reals, complex, and quaternionic numbers).
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This stratal geometry is common in temperate carbonates.
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Among the subjects to which his principal papers related were plane and solid geometry, theory of numbers, and link motion.
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The bulk elastic modulus of the collagen gels was measured using a stress-controlled rheometer with a 4°, 40-mm cone and plate geometry.
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Van Dijk et al. emphasized the absence of deep erosional incision in the geometry of the unconformity.
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The geometry of the cantilever construction was controlled primarily by applying a high degree of precision and maintaining very close tolerances on the prefabricated components used on the main span.
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Can we predict the temperature profile from the known geometry and heat conduction of water?
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This led to a series of two-sided drawings - it didn't matter to the artist which side was shown - that explored what she calls paper's ‘natural geometry.’
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On one particular occasion, she challenged the group to solve a curious problem in plane geometry that she had recently encountered.
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Whether the path to unification will be via the geometrization of physics is a moot point since one cannot define the boundaries of geometry.
RELATIVITY
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To do this, he advanced the study of differential equations from numbers, formulas, and the manipulation of algebraic equations to geometry, curves, and the visualization of flows.
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His great love within mathematics was geometry, and this turned out to be his lifelong field.
Times, Sunday Times
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However, accuracy of the position estimate by triangulation may be degraded depending on array geometry and rover location, the well known dilution of precision.
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The second chapter presents a development of absolute and Euclidean geometry based on Hilbert's axioms.
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The main living area is open plan and bathed in light from the tall windows, and the geometry of this window formation is echoed within the structure of the space.
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The perspective of three-dimensional objects in the two-dimensional image is dictated by the viewing geometry and the camera.
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Celestial mechanics is the origin of dynamical systems, linear algebra, topology, variational calculus and symplectic geometry.
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He was always full of mathematical ideas, not only on game theory, but in geometry and topology as well.
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At Freiburg, he took a course with Oskar Bolza on the theory of invariants, and a course on differential geometry and a history seminar with Alfred Loewy, one of the two professors at Freiburg.
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Capturing all the physics involved affects the final panel quality and geometry after trimming, springback, and flanging.
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She was particularly perplexed by geometry; she aroused our hilarity by always calling a parallelogram a parallel-O-gram, with a strong emphasis on the penultimate syllable; and she spent several days repeating over to herself, with a mystified countenance, the famous words, "The square of the hypothenuse is equal to the sum of the squares of the two legs.
Hawthorne and His Circle
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The practice of drawing and painting offers the student the following problem in descriptive geometry: _to represent the three dimensions of space by means of a plane surface of two dimensions_.
Chinese Painters A Critical Study
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The rheology of BLG solutions at 20°C was determined using a Rheometrics rheometer with parallel plate geometry.
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Karl Gauss pioneered hyperbolic geometry
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Why do I refer to Euclidean geometry as a physical theory rather than a branch of mathematics?
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The book contained the elements of geometry and algebra in addition to the calculus.
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A proposed geometry of the LacI loop as a tight supercoil away from the protein has been controversial, and it is likely that loop geometry is different for different DNA sequences.
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When the coefficients of quadratic equations were irrational numbers, Abu Kdmil abandoned the geometry demonstration showing the trend of arithmetization.
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This, with your physics, your geometry, and your exercises, will be all that you can possibly have time for at Paris; for you must allow a great deal for company and pleasures: it is they that must give you those manners, that address, that 'tournure' of the 'beau monde', which will qualify you for your future destination.
Complete Project Gutenberg Earl of Chesterfield Works
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In 1940 he introduced the concept of an injective module, then began studying group actions in geometry.
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For example, algebraic geometry, the field I am most familiar with, combines algebra, geometry, topology, and analysis.
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If the mind, with greater facility, retains the ideas of geometry clear and determinate, it must carry on a much longer and more intricate chain of reasoning, and compare ideas much wider of each other, in order to reach the abstruser truths of that science.
An Enquiry Concerning Human Understanding
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The effectiveness of the quench will depend primarily on two factors: the geometry of the specimen, and the composition of the steel.
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Like conventional rendering, the scene is passed to the geometry processing engine where the polygons are transformed into view space.
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Euclid's axioms form the foundation of his system of geometry.
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Centuries later, Jews would repay the compliment by appropriating the Greek word geometry and creating the word gematria, which is Hebrew for
Mental_floss Blog
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Now we can create an additional function that will combine the before mentioned functions and produce the scalar value on the space filling z-curve for any given geometry.
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But ‘partial’ eyes turn out to be common in nature, and biologists can trace eye evolution from the lensless flatworm eyespot to the complex geometry of vertebrate eyes.
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Not being a whiz at geometry, I stared at the pattern for quite a while trying to figure out the formula for measuring the degrees of the angles.
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But he was the first ever to appreciate, demonstrate and exploit the utility of completely integrable systems of linear homogeneous differential equations for projective differential geometry.
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The jagged geometry of supersmooth Europa; the idiosyncratic surfaces of the other orbs floating serenely in space; the pristine interstellar vacuum; the inscrutable emptiness of intergalactic space, that immense, echoing, absolutely featureless void enveloping the spinning galaxies: it all serves as a perfect philosophical mirror image, reflecting back the quandary of the species, the limitations of human knowledge.
A Space in Time
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Most CAD products include one or all of these translators it be geometry, structure, attributes, or associativity. at no additional cost • Direct translators that work in the background to allow one Siemens PLM Software is the only company that can provide this level product to open native files from another without any visible of interoperability. intermediate step.
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Geometry, and its branch trigonometry, was the mathematics Indian astronomers used most frequently.
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There, up above the concrete geometry, you'll find a sheltered suntrap with stunning views, and somewhere lush, green and growing.
Telegraph.co.uk - Telegraph online, Daily Telegraph and Sunday Telegraph
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The Journal of Topology publishes papers of high quality and significance in topology, geometry, and adjacent areas of mathematics.
November 2007
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Cramer taught geometry and mechanics while Calandrini taught algebra and astronomy.
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After an explosion, the site was resurveyed and sectioned by deep trenches so that the geometry of various structures and ground movement that resulted could be accurately established.
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Secondly, I am working on the history of dioptrics, the geometry of the projections, as well as on the theory of conics.
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A study of primary school pupils suggested some would be good at geometry but not algebra so they needed to practise the weaker subject more.
The Sun
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His greatest fame, however, is as a result of the mathematical models which he created to assist in his teaching of geometry.
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The loose geometry suggests a kind of preindustrial masonry or fabric patterning, while the range of colors defies generalization.
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For Plato himself, a study of mathematics and geometry leads the mind away from the corruptible and perishable to the contemplation of true Being and eternal order.
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Weil's work on bringing together number theory and algebraic geometry was highly fruitful.
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The geometry is meshed with a mapping algorithm or an automatic free-meshing algorithm.
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SOCRATES: And when we compare the art of mensuration which is used in building with philosophical geometry, or the art of computation which is used in trading with exact calculation, shall we say of either of the pairs that it is one or two?
Philebus
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So when Euclid described his geometry, many believed it to be the one true geometry.
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There is no evidence of any previous doming, and the fault geometry indicates that the rift formed as a result of horizontal extension perpendicular to the rift axis.
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You cannot write a text-book of geometry without reference to a hypotenuse and triangles and a rectangular parallelopiped.
The Story of Mankind
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They should also be able to understand basic maths and geometry, including fractions, decimals, multiplication and division.
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In particular he made contributions of major importance in the theory of polytopes, non-euclidean geometry, group theory and combinatorics.
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To illustrate with one example, the work of Hippocrates on the quadrature of lunes is only known to us through Eudemus's History of Geometry.
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The use of elementary geometry method can give conformal demonstration of lineal function in infinite eigenvector.
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The sparse, tilelike geometry of a 2009 work by Bernard Piffaretti parses the voluptuous blues and greens of a 1977 canvas by Joan Mitchell.
NYT > Home Page
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The most common geometry for curved crystal diffraction is based on the Rowland circle principle, which relies on the well-known property of a circle that an arc segment subtends a constant angle for any point on the circle.
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The bottom portion of the frame is populated by the complex geometry and sprites that make up the environment, while the top portion contains some geometry and the large sky box.
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Vertex instancing allows the geometry for say, 100 of these models to be batched into an array, and sent down all at once.
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Much of his career is spent working on physics and non-euclidean geometry.
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He introduced the word pole in projective geometry.
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For top-down and thin-wall part design, the Indent feature lets you add geometry or form a recess based on a tool body.
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Also on the anvil are a Braille slate, abacus for mathematics, geometry set with raised numbers and an alphabet plate to enable the visually impaired to learn to write.
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This process is similar to constructing a proof in geometry: the author knows the conclusion before writing the proof, but in the proof, the conclusion follows from the logic and not just the say-so of the author.
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The appearance of fractal geometry extended our former understanding about dimension and scale of architecture.
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Since Euclid's axiomatic formulation of geometry mathematicians had been trying to prove his fifth postulate as a theorem deduced from the other four axioms.
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The proportionality constant M is provided and its variation with geometry and Biot number ( ? ? ) is discussed.
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König worked on a wide range of topics in algebra, number theory, geometry, set theory, and analysis.
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A better approach is to integrate the three stages into a highly compact, free-space geometry.
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Beltrami, in 1868, gave a concrete realisation of Lobachevsky's geometry.
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This work was to be in four parts, arithmetic, geometry, mechanics, and hydraulics.
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In the course of the last sixty years, many new sciences have taken their place in the category of our knowledge, among which is stereotomy, descriptive geometry, and the chemistry of gas.
The physiology of taste; or Transcendental gastronomy. Illustrated by anecdotes of distinguished artists and statesmen of both continents by Jean Anthelme Brillat-Savarin. Translated from the last Paris edition by Fayette Robinson.
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Artists and geometry In the history of painting many pictures have been based on simple geometric designs.
Improve Your Landscape Painting
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To illustrate this viewpoint, several topics taken from elementary geometry are carefully analyzed.
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Thus, this conjecture of Artin was the origin of a wide range of activities in what is now called arithmetic geometry.
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With an understanding that somehow goes beyond his years, he intuits the nuances of the game, its geometry, its very nature.
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The shortlist is completed by The Changing World of Inflammatory Bowel Disease and Crocheting Adventures with Hyperbolic Planes, which informs its readers how to "crochet models of the hyperbolic plane, pseudosphere, and catenoid/helicoids", as well as exploring geometry and its historical connections with art, architecture, navigation and motion, and the history of crochet.
Culture | guardian.co.uk
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Apparently the monocyclic geometry leads to stronger interactions between peptide and chromophore extending also to longer times.
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The trivium consisted of grammar, logic and rhetoric, the quadrivium of arithmetic, geometry, astronomy and music.
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In concern of the controversy caused by the expurgation of plane geometry in the new high school math textbook, we spend one year penetrating deeply in this area.
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His writings on geometry included several important papers on parallel curves and surfaces.
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Artists and geometry In the history of painting many pictures have been based on simple geometric designs.
Improve Your Landscape Painting
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Additionally, the well—known four colour problem and elementary geometry theorem—proving problem have been discussed.
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Euclidean geometry studies Euclidean-space-structure, topology studies topological structures, and so on.
