noun বিশেষ্য পদ

# Affine geometry meaning in assamese

### affine জ্যামিতি

• Definition

the geometry of affine transformations

এফিন ৰূপান্তৰৰ জ্যামিতি

noun বিশেষ্য পদ

## Affine geometry meaning in assamese

### affine জ্যামিতি

• Definitions

1. The branch of geometry dealing with what can be deduced in Euclidean geometry when the notions of line length and angle size are ignored.

ৰেখাৰ দৈৰ্ঘ্য আৰু কোণৰ আকাৰৰ ধাৰণাক আওকাণ কৰিলে ইউক্লিডীয় জ্যামিতিত কি অনুমান কৰিব পাৰি তাৰ সৈতে জড়িত জ্যামিতিৰ শাখা।

• Examples:
1. As an alternative to the axiomatic approach, affine geometry can be studied via the properties of affine transformations, which do not, in general, preserve distances or angles, but do preserve alignment of points and parallelism of lines.\$V\$The notion of parallelism remains central to affine geometry, in which the parallel postulate is replaced by Playfair's axiom, a version of the postulate that relies on neither distance nor angle size.

2. Affine geometry is the geometry of an n-dimensional vector space together with its inhomogeneous linear structure. Arbitrary affine linear maps take affine linear subspaces into one another, and also preserve collinearity of points, parallels and ratios of distances along parallel lines; all these are thus well defined notions of affine geometry.

3. And affine geometry itself can be considered as the geometry of all projective transformations which leave a line invariant.

4. To include affine geometry, Menger (1935) imposed on lattices a reasonable axiom of parallelism.

• 2. A geometry that is otherwise Euclidean but disregards lengths and angle sizes.

এনে জ্যামিতি যি অন্যথা ইউক্লিডিয়ান কিন্তু দৈৰ্ঘ্য আৰু কোণৰ আকাৰক অৱজ্ঞা কৰে।

• Examples:
1. The affine geometry A G ( n , F ) {\displaystyle {AG}(n,F)} is obtained from P G ( n , F ) {\displaystyle {PG}(n,F)} [a projective geometry] by deleting from the latter all the points of a hyperplane.

2. This chapter is devoted to the theory of affine geometries: those incidence geometries which satisfy the Euclidean parallel postulate in Playfair's form (Ch. 2, Sec. 2).

3. We here review work on the discretization of affine geometries which was undertaken in collaboration with A. I. Bobenko [7, 8, 37].