# Monthly Archives: September 2020

## Quasi Metric for Generalization of Epsilon net

Here we mention the definition of -net that came in the paper “Randomized Incremental Construction of Delaunay Triangulations of Nice Point Sets” by Jean-Daniel Boissonnat, Olivier Devillers, Kunal Dutta & Marc Glisse ; Assum is a set of points in a metric space . -packing: is an -packing if any pair of points in are… Read More »

## VC dimension of TOP-set system

Here we mention the definition of VC–dimension that came in the paper “A Simple Proof of Optimal Epsilon Nets” by Nabil H. Mustafa, Kunal Dutta & Arijit Ghosh; Given and any set , define the projection of onto as the set system: The VC dimension of is the size of the largest subset Y for… Read More »

## Set System with Topology; TOP-set system

Here we mention the definition of Set System that came in the paper “Epsilon-approximations and epsilon-nets” by Nabil H. Mustafa and Kasturi R. Varadarajan; A pair , where is a set of base elements and is a collection of subsets of , is called a set system. Question: ‎If ‎ ‎be a set system‎, can… Read More »

## Wu’s Method

Here is the summary of last section; section 5 of Chapter 6; Robotics and Automatic Geometric Theorem Proving of the book {Ideals, Varieties, and Algorithms} By‎ David A. Cox , John Little and Donal O’Shea Here we want to introduce an algorithmic method for proving theorems in Euclidean geometry based on systems of polynomial equations.… Read More »

## Automatic Geometric Theorem Proving

Here is the summary of section 4 of Chapter 6; Robotics and Automatic Geometric Theorem Proving of the book {Ideals, Varieties, and Algorithms} By‎ David A. Cox , John Little and Donal O’Shea Here we intend to introduce this idea that the hypotheses and conclusions of a large class of geometric theorems can be expressed… Read More »

## Inverse Kinematic Problem

Here is the summary of section 3 of Chapter 6; Robotics and Automatic Geometric Theorem Proving of the book {Ideals, Varieties, and Algorithms} By‎ David A. Cox , John Little and Donal O’Shea The ‎problem ‎is:‎‎‎ Given‎ ‎ , ‎can ‎we ‎determine ‎one ‎or ‎all ‎the‎ ‎ ‎such ‎that‎ ‎ ?‎‎‎ Indee‎d ‎‎we wish to… Read More »

## The Forward Kinematic Problem

Here is the summary of section 2 of Chapter 6; Robotics and Automatic Geometric Theorem Proving of the book {Ideals, Varieties, and Algorithms} By‎ David A. Cox , John Little and Donal O’Shea The Forward Kinematic Problem Can ‎we ‎give ‎explicit ‎description ‎or ‎formula ‎for‎ in terms of the joint setings (our coordinates on ‎… Read More »

## Geometric Description of Robots

Here is the summary of section 1 of Chapter 6; Robotics and Automatic Geometric Theorem Proving of the book {Ideals, Varieties, and Algorithms} By‎ David A. Cox , John Little and Donal O’Shea Types of Robots Here we aim to study some special types of robots that can describe as below: 1. Robots in which… Read More »