MAVZU: N-O’LCHOVLI FAZODAGI FIGURALAR
Keywords:
Kalit so‘zlar: n-o‘lchovli figuralar, n-o‘lchovli fazo, giper-kub, giper-shar, fazoviy jismlar, geometrik o‘lchov, gamma-funksiya, ℝⁿ fazo, ko‘p o‘lchovli geometriya, hajm, yuzasi, fazoviy model, matematika, Coxeter, Regular Polytopes., Keywords: n-dimensional figures, n-dimensional space, hypercube, hypersphere, spatial solids, geometric dimension, gamma function, ℝⁿ space, multidimensional geometry, volume, surface area, spatial model, mathematics, Coxeter, Regular Polytopes.Abstract
Anotatsiya:“n-o‘lchovli fazoda figuralar” mavzusi geometriya va chiziqli algebraga asoslanib, fazoning istalgan o‘lchamida joylashgan geometrik jismlarni, ularning xossalari va o‘zaro bog‘liqliklarini o‘rganadi. n-o‘lchovli fazo deganda har bir nuqtasi n ta koordinata bilan aniqlanadigan fazo tushuniladi. Bunday fazoda figuralar vektorlar va tenglamalar orqali ifodalanadi, masalan, to‘g‘ri chiziq parametrik tenglama, gipertekislik esa chiziqli tenglama yordamida aniqlanadi. Mavzu matematikaning turli sohalari, jumladan, fizika, informatika, statistika va sun’iy intellektda keng qo‘llaniladi. U ko‘p o‘lchovli tizimlarni modellashtirish, ma’lumotlarni tahlil qilish va murakkab jarayonlarni tushuntirishda muhim ahamiyat kasb etadi. N-o‘lchovli fazoda figuralarni o‘rganish fazoviy tafakkurni kengaytiradi va matematik tushunchalarni umumlashtirish imkonini beradi.
Annotation:“Figures in n-dimensional space” is based on geometry and linear algebra, focusing on the study of geometric objects in spaces of any dimension, their properties, and interrelations. An n-dimensional space is defined as a space in which each point is determined by n coordinates. In such spaces, figures are represented using vectors and equations — for example, a line can be expressed through a parametric equation, while a hyperplane is defined by a linear equation. This topic has wide applications in various fields such as physics, computer science, statistics, and artificial intelligence. It plays an important role in modeling multidimensional systems, analyzing data, and explaining complex processes. Studying figures in n-dimensional space helps to broaden spatial thinking and generalize mathematical concepts to higher dimensions.
