Measuring quadric sectors at centre

TL;DR

This paper investigates sectors at the center of affine quadrics with point symmetry over various fields, providing formulas for their area and volume, filling a gap in the existing research.

Contribution

It introduces new formulas for the area and volume of sectors in affine quadrics with point symmetry, expanding understanding beyond previously studied special cases.

Findings

Derived formulas for sector area in planar affine quadrics.

Established volume formulas for spatial sectors.

Extended analysis to arbitrary fields of characteristic not two.

Abstract

Sectors at centre of affine quadrics with point symmetry are investigated over arbitrary fields of characteristic different from two. As an application we demonstrate nice formulas for the area and the volume of such planar and spatial sectors, respectively, in euclidean space. It seems that up to now there has been atmost little research in this field up to very special cases.