英语词汇“projective geometry”造句的方法、技巧、例句及翻译-英语例句辞典

Every theorem in Euclidean geometry can be dualized in projective geometry, setting up a whole set of new theorems in the parallel universe of projective geometry. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z

The first development—projective geometry—was born in the turmoil of war. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z

However, Poncelet had no idea that projective geometry would reveal the mysterious nature of zero, because the second important advance, the complex plane, was still needed. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z

Riemann merged projective geometry with the complex numbers, and all of a sudden lines became circles, circles became lines, and zero and infinity became the poles on a globe full of numbers. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z

Moldering in a Russian prison, Poncelet founded a new discipline: projective geometry. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z

This was the beginning of the discipline of projective geometry, where mathematicians look at the shadows and projections of geometric figures to uncover hidden truths even more powerful than the equivalence of parabolas and ellipses. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z

These undetermined ideas take different specific meanings for the various specific subject matters to which projective geometry can be applied. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z

And this is true even of such apparently essentially intuitional fields as projective geometry, where entities can be substituted for directional lines and the axioms be turned into relational postulates governing their configurations. Creative Intelligence Essays in the Pragmatic Attitude

The author is professor of projective geometry and geometric drawing in the University of Bologna, and is one of the most conspicuous of contemporary Italian scientists. A Mechanico-Physiological Theory of Organic Evolution

He also published several papers on algebraic forms and projective geometry. Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 5 "Clervaux" to "Cockade"

This correspondence is of such fundamental importance in the study of projective geometry that a special name is given to it. An Elementary Course in Synthetic Projective Geometry

Thus, if we choose to take any one of these three theorems as an axiom, all the theorems of projective geometry which do not require ordinal or metrical ideas for their enunciation can be proved. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z

Four-dimensional geometry yields numberless other patterns whose beauty and interest could not possibly be impeached—patterns beyond the compass of the cleverest designer unacquainted with projective geometry. Architecture and Democracy

By thus realizing the source in man of the polar-Euclidean thought-forms, we see the discovery of projective geometry in a new light. Man or Matter

A second important advance followed the recognition that conics could be regarded as projections of a circle, a conception which led at the hands of Desargues and Pascal to modern projective geometry and perspective. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z

A final word is necessary in order to explain a phrase which is in constant use in the study of projective geometry. An Elementary Course in Synthetic Projective Geometry

In projective geometry any two straight lines in a plane intersect, and the straight lines are closed series which return into themselves, like the circumference of a circle. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z

The others are said to be projective properties, and their investigation forms the subject of projective geometry. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z

In projective geometry the operation is of a different character. Man or Matter

Projective Geometry It is difficult, at the outset, to characterize projective geometry as compared with Euclidean. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z

His method is extremely interesting, and will serve as an exercise for the student in synthetic projective geometry. An Elementary Course in Synthetic Projective Geometry

Ordinary Euclidean geometry is a descriptive geometry; it becomes a projective geometry when the so-called “points at infinity” are added. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z

Conceived dynamically, as projective geometry requires, Point and Plane represent a pair of opposites, the Point standing for utmost contraction, the Plane for utmost expansion. Man or Matter

单词	projective geometry
例句	projective geometry Every theorem in Euclidean geometry can be dualized in projective geometry, setting up a whole set of new theorems in the parallel universe of projective geometry. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z The first development—projective geometry—was born in the turmoil of war. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z However, Poncelet had no idea that projective geometry would reveal the mysterious nature of zero, because the second important advance, the complex plane, was still needed. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z Riemann merged projective geometry with the complex numbers, and all of a sudden lines became circles, circles became lines, and zero and infinity became the poles on a globe full of numbers. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z Moldering in a Russian prison, Poncelet founded a new discipline: projective geometry. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z This was the beginning of the discipline of projective geometry, where mathematicians look at the shadows and projections of geometric figures to uncover hidden truths even more powerful than the equivalence of parabolas and ellipses. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z These undetermined ideas take different specific meanings for the various specific subject matters to which projective geometry can be applied. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z And this is true even of such apparently essentially intuitional fields as projective geometry, where entities can be substituted for directional lines and the axioms be turned into relational postulates governing their configurations. Creative Intelligence Essays in the Pragmatic Attitude The author is professor of projective geometry and geometric drawing in the University of Bologna, and is one of the most conspicuous of contemporary Italian scientists. A Mechanico-Physiological Theory of Organic Evolution He also published several papers on algebraic forms and projective geometry. Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 5 "Clervaux" to "Cockade" This correspondence is of such fundamental importance in the study of projective geometry that a special name is given to it. An Elementary Course in Synthetic Projective Geometry Thus, if we choose to take any one of these three theorems as an axiom, all the theorems of projective geometry which do not require ordinal or metrical ideas for their enunciation can be proved. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z Four-dimensional geometry yields numberless other patterns whose beauty and interest could not possibly be impeached—patterns beyond the compass of the cleverest designer unacquainted with projective geometry. Architecture and Democracy By thus realizing the source in man of the polar-Euclidean thought-forms, we see the discovery of projective geometry in a new light. Man or Matter A second important advance followed the recognition that conics could be regarded as projections of a circle, a conception which led at the hands of Desargues and Pascal to modern projective geometry and perspective. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z A final word is necessary in order to explain a phrase which is in constant use in the study of projective geometry. An Elementary Course in Synthetic Projective Geometry In projective geometry any two straight lines in a plane intersect, and the straight lines are closed series which return into themselves, like the circumference of a circle. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z The others are said to be projective properties, and their investigation forms the subject of projective geometry. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z In projective geometry the operation is of a different character. Man or Matter Projective Geometry It is difficult, at the outset, to characterize projective geometry as compared with Euclidean. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z His method is extremely interesting, and will serve as an exercise for the student in synthetic projective geometry. An Elementary Course in Synthetic Projective Geometry Ordinary Euclidean geometry is a descriptive geometry; it becomes a projective geometry when the so-called “points at infinity” are added. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z Conceived dynamically, as projective geometry requires, Point and Plane represent a pair of opposites, the Point standing for utmost contraction, the Plane for utmost expansion. Man or Matter
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