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One of the underlying insights of topology is that some geometric problems depend not on the precise shape of objects but only on the way they are connected.
Methods for precise geometric descriptions, necessary for visualization, were formulated later.
They also serve to illustrate why it is easy to confuse the various geometric forms represented by sets of numeric indices unless one is aware of these conventions.
In 1984 Jones discovered an astonishing relationship between von Neumann algebras and geometric topology.
A simple example of numerical integration is estimating the area of a geometric figure by randomly throwing darts at it and counting the hits and misses.
Apollonius used his geometric skills to mathematically develop the epicycle theory which would reach its full importance in the work of Ptolemy.
Normal maps are used to give additional geometric detail without increasing polygon count.
Omar Khayyam gave a complete classification of cubic equations with geometric solutions found by means of intersecting conic sections.
There is, of course, a tension in this topic between the totally geometric approach and the algebraic approach.
He also focuses on using geometric algebra to solve problems in graph theory.
In addition, C is only a geometric parameter to describe gross shell morphology, rather than a biological determinant.
Although I'm reasonable at mental arithmetic, I mostly think geometrically and then must laboriously check my geometric intuition with algebra.
We used a geometric method called eigenshape analysis to quantify turritellid shell morphology.
This is a remarkable mathematical theory combining powerful algebraic and geometric methods.
In 1849 he published Trigonometry and double algebra in which he gave a geometric interpretation of complex numbers.
Thus in a sense all cubics could be solved by the Greeks using geometric methods.
This discovery was made as Möbius worked on a question on the geometric theory of polyhedra posed by the Académie.
The Billera-Lee proof gives a geometric construction of one simplicial polytope for each face vector.
He developed a theory of automorphic functions, connecting algebraic and geometric results in his important 1884 book on the icosahedron.
In the next 2000 years no one found an exact geometric method for 7-gons or 9-gons but also no one had proved it was impossible to construct such regular polygons.
2
(pattern/shape)geométrico
Linen looks best in simple shapes, with clean geometric lines.
Its form was a beautiful display of geometric symmetry.
In four new paintings comprising his recent solo show, ribbons give way to a system of lines and ovoid shapes contained within large geometric fields of color.
There is also a beautiful image of Mondrian's studio, reduced to geometric lines just like a painting in the famous mature Mondrian style.
The old gentleman places a rug, decorated with geometric animals, on the ground and invites me to sit.
These tiles are characterized by slender lines, geometric shapes, or more free-form patterns.
The result is a remarkably regular, geometric pattern, as his two untitled pieces from 1997 demonstrate.
In stunning detail, pilots and crew describe a range of geometric forms and lights inconsistent with known aircraft or natural phenomena.
On this magnificent necklace, worn by either a young woman or man, the beadworker has skillfully played with colors and geometric shapes.
Zanzibar doorways, decorated with geometric patterns, offer a glimpse of the island's Arabic history and tradition.
I opened my eyes to a net of pale blue moonlight and shadows thrown across whitewashed walls and ceiling decorated with geometric bas-reliefs in cracked and stained plaster.
Libyan artisans use intricate lines and geometric shapes in their carpets, embroidered goods, jewelry, leather goods, tiles, and pottery.
The geometric shapes and patterns rendered in pencil, ink and watercolor on graph paper are suggestive of spiritual emblems taken from a variety of religions.
Sets of geometric shapes painted in attractively unnatural enamel colors, the paintings are composed with horizon lines and often light grounds.
Quilting designs may carry across the quilt ignoring seam lines in fancy or plain geometric patterns.
Lemmer's geometric, symmetrical sculptures are clearly variations on a theme.
This season, bold geometric shapes are omnipresent, with various lines in particular adding rhythm and exuberance to the fabrics.
Dr. Just said that the brain could interpret letters either spatially, as geometric shapes, or linguistically, by the names of the letters.
My newer ties are splashier, with brightly colored splotches, wildly zigzagging lines, and unusual geometric shapes.
Analysis of protein loop conformations is a notoriously difficult task because they do not have easily identifiable regular geometric patterns.