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Chapter 3: Figurate Numbers
This document discusses different types of figurate numbers including triangular, square, pentagonal, and hexagonal numbers. It provides examples of the patterns formed by each type of number and formulas to calculate the nth term. Relations between different figurate numbers are also explored, such as how the 4th square number can be expressed as the sum of the 3rd and 4th triangular numbers. A brief history of polygonal numbers is given, noting they were first studied by Pythagoras.
Square numbers & exponents
This document discusses square numbers and exponents. Square numbers are the product of a number multiplied by itself, such as 4 x 4 = 16. Numbers are not square if they are the product of two different numbers, like 6 x 4. Exponents represent how many times a base number is used as a factor, so 5^3 means 5 multiplied by itself 3 times, which equals 125. The document provides examples and definitions of square numbers and exponents to build understanding of these mathematical concepts.
Charles Sturt University - Student Mentor
Doctor of Information Technology, Charles Sturt University - 2013 - 2016
Effective research planning and execution using Scopus and ScienceDirect
This certificate of attendance certifies that Chinnaraji Annamalai attended a training on effective research planning and execution using Scopus and ScienceDirect at University of Jammu on Friday, December 17, 2021. The training was presented by Vishal Gupta, a senior customer consultant at Elsevier, and signed by Suzanne BeDell, Managing Director of Education at Elsevier, and Philippe Terheggen, Managing Director of Science, Technology & Medical Journals at Elsevier.
Certificate on Wastewater Remediation and Management with Nanotechnology
Dr. C. Annamalai from IIT Kharagpur received a Certificate of Participation for actively participating in the National Webinar on 'Trends in Wastewater Remediation and Management with Nanotechnology' jointly organized by the National Centre for Nanoscience and Nanotechnology and Centre for Water Resources Management at the University of Madras on April 9, 2021. The certificate was issued and signed by the convenors G. Bhaskaran and S. Balakumar from the University of Madras.
Recommended
Chapter 3: Figurate Numbers
This document discusses different types of figurate numbers including triangular, square, pentagonal, and hexagonal numbers. It provides examples of the patterns formed by each type of number and formulas to calculate the nth term. Relations between different figurate numbers are also explored, such as how the 4th square number can be expressed as the sum of the 3rd and 4th triangular numbers. A brief history of polygonal numbers is given, noting they were first studied by Pythagoras.
Square numbers & exponents
This document discusses square numbers and exponents. Square numbers are the product of a number multiplied by itself, such as 4 x 4 = 16. Numbers are not square if they are the product of two different numbers, like 6 x 4. Exponents represent how many times a base number is used as a factor, so 5^3 means 5 multiplied by itself 3 times, which equals 125. The document provides examples and definitions of square numbers and exponents to build understanding of these mathematical concepts.
Charles Sturt University - Student Mentor
Doctor of Information Technology, Charles Sturt University - 2013 - 2016
Effective research planning and execution using Scopus and ScienceDirect
This certificate of attendance certifies that Chinnaraji Annamalai attended a training on effective research planning and execution using Scopus and ScienceDirect at University of Jammu on Friday, December 17, 2021. The training was presented by Vishal Gupta, a senior customer consultant at Elsevier, and signed by Suzanne BeDell, Managing Director of Education at Elsevier, and Philippe Terheggen, Managing Director of Science, Technology & Medical Journals at Elsevier.
Certificate on Wastewater Remediation and Management with Nanotechnology
Dr. C. Annamalai from IIT Kharagpur received a Certificate of Participation for actively participating in the National Webinar on 'Trends in Wastewater Remediation and Management with Nanotechnology' jointly organized by the National Centre for Nanoscience and Nanotechnology and Centre for Water Resources Management at the University of Madras on April 9, 2021. The certificate was issued and signed by the convenors G. Bhaskaran and S. Balakumar from the University of Madras.
Certificate on Computer Science, The Institute of Mathematical Sciences Chennai
Summer School on Theoretical Aspects of Computer Science conducted by Theoretical Computer Science Unit of the Institute of Mathematical Sciences.
Training Program
The document provides an agenda for a valedictory function to conclude a 5-S training program at the Indian Institute of Technology Kharagpur on March 27, 2021. The event will include welcome and opening remarks, presentations by participating department leaders, speeches by guest trainers and institute officials, and closing remarks. It will take place from 10 AM to 12 PM in the Raman Auditorium.
Niripeyarchy
Dr. Chinnaraji Annamalai of the Indian Institute of Technology Kharagpur introduces the new concept of "niripeyarchy" in theoretical physics. Niripeyarchy is defined as the product of an object's displacement and mass, and has SI units of kg m. Momentum is defined as the rate of change of niripeyarchy and has units of kg m/s. Force is then defined as the rate of change of momentum, having units of kg m/s^2. Niripeyarchy and related concepts are introduced to better define momentum and its relationships to displacement, mass, velocity, and force.
BHARAT JYOTI AWARD
Honoured me with “Bharat Jyoti Award & Certificate of Excellence” for Meritorious Services, Outstanding Performance and Remarkable Role.
Facts
Thinking leads to knowledge which drives research through the human mind. Research then enables technology, and technology facilitates development. Development cultivates great people who can advance a nation to become a developed country. Natural phenomena provoke inquiry in human minds to understand underlying facts. Those who uncover these factual explanations are considered scientists, and scientists can then engineer technologies to address contemporary issues.
WHAT? WHY? HOW?
The document discusses how asking "what, why, how" questions about natural phenomena can generate ideas and lead to acquiring knowledge through analysis. Obtaining clear information from experimental work using this knowledge produces facts about natural events. These discovered facts can then be reused through research to develop technology. The document presents research as reusing discovered facts to develop technology, with the relationship that facts plus research equals technology.
My Webpage on IIT Kharagpur
This document provides biographical and contact information for C Annamalai, an Assistant Registrar at Vinod Gupta School of Management at IIT Kharagpur. It lists his education, areas of research, awards, publications, text books he has reviewed, patents, copyrights, membership in professional organizations, and contact details.
WINNER OF 2007 CIU OUTSTANDING PROFESSIONAL ( C.O.P ) AWARD
C Annamalai - CCDA
Mahesh Ravindran - CCDA
Michael Vagionakis - CCSA
Sukhjinder Pal Singh - CCSA
Naveen B. - CCWA
Handoko - CCWA
Andre M - CCLA
Jonathan Yaniv - CCLA
Michael Vagionakis - CSSecA
Goumenidis Theodoros - PC Support
Harsha Bagur - VOIP Project
Dodecahedral pentagonal polytopes
This document discusses various polytopes defined by Coxeter groups and their Schläfli symbols. It provides information on the order of the Coxeter groups, the Schläfli symbols that define each polytope, and counts of their facets, vertices, edges, faces and cells. The polytopes range from a line segment and pentagon to the dodecahedron, 120-cell, and a honeycomb of 120-cells.
Euler diagram for P, NP, NP-complete, and NP-hard set of problems
If there is a polynomial algorithm for any NP-hard problem, then there are polynomial algorithms for all problems in NP, and hence P = NP.
If P ≠ NP, then NP-hard problems cannot be solved in polynomial time, while P = NP does not resolve whether the NP-hard problems can be solved in polynomial time;
IEEE Certificate
Prof. C. Annamalai completed a course titled "System and User Space Virtualization Support in Yocto - the Yocto MetiVirtualization Project" on March 26, 2013 and earned 1 professional development hour.
NASA Certificate for My "Face in Space"
This certificate certifies that a face likeness of Chinnaraji Annamalai flew aboard the Space Shuttle Discovery on its STS-133 mission from February 24 to March 9, 2011. The face flew at an altitude of 220 miles above Earth and an orbital speed of over 17,400 miles per hour delivering supplies to the International Space Station. The NASA crew thanked Chinnaraji Annamalai for sharing in the excitement of the mission and exploration of space.
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
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Natural birth techniques are various type such as/ water birth , alexender method, hypnosis, bradley method, lamaze method etcExecutive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
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Certificate on Computer Science, The Institute of Mathematical Sciences Chennai
Summer School on Theoretical Aspects of Computer Science conducted by Theoretical Computer Science Unit of the Institute of Mathematical Sciences.
Training Program
The document provides an agenda for a valedictory function to conclude a 5-S training program at the Indian Institute of Technology Kharagpur on March 27, 2021. The event will include welcome and opening remarks, presentations by participating department leaders, speeches by guest trainers and institute officials, and closing remarks. It will take place from 10 AM to 12 PM in the Raman Auditorium.
Niripeyarchy
Dr. Chinnaraji Annamalai of the Indian Institute of Technology Kharagpur introduces the new concept of "niripeyarchy" in theoretical physics. Niripeyarchy is defined as the product of an object's displacement and mass, and has SI units of kg m. Momentum is defined as the rate of change of niripeyarchy and has units of kg m/s. Force is then defined as the rate of change of momentum, having units of kg m/s^2. Niripeyarchy and related concepts are introduced to better define momentum and its relationships to displacement, mass, velocity, and force.
BHARAT JYOTI AWARD
Honoured me with “Bharat Jyoti Award & Certificate of Excellence” for Meritorious Services, Outstanding Performance and Remarkable Role.
Facts
Thinking leads to knowledge which drives research through the human mind. Research then enables technology, and technology facilitates development. Development cultivates great people who can advance a nation to become a developed country. Natural phenomena provoke inquiry in human minds to understand underlying facts. Those who uncover these factual explanations are considered scientists, and scientists can then engineer technologies to address contemporary issues.
WHAT? WHY? HOW?
The document discusses how asking "what, why, how" questions about natural phenomena can generate ideas and lead to acquiring knowledge through analysis. Obtaining clear information from experimental work using this knowledge produces facts about natural events. These discovered facts can then be reused through research to develop technology. The document presents research as reusing discovered facts to develop technology, with the relationship that facts plus research equals technology.
My Webpage on IIT Kharagpur
This document provides biographical and contact information for C Annamalai, an Assistant Registrar at Vinod Gupta School of Management at IIT Kharagpur. It lists his education, areas of research, awards, publications, text books he has reviewed, patents, copyrights, membership in professional organizations, and contact details.
WINNER OF 2007 CIU OUTSTANDING PROFESSIONAL ( C.O.P ) AWARD
C Annamalai - CCDA
Mahesh Ravindran - CCDA
Michael Vagionakis - CCSA
Sukhjinder Pal Singh - CCSA
Naveen B. - CCWA
Handoko - CCWA
Andre M - CCLA
Jonathan Yaniv - CCLA
Michael Vagionakis - CSSecA
Goumenidis Theodoros - PC Support
Harsha Bagur - VOIP Project
Dodecahedral pentagonal polytopes
This document discusses various polytopes defined by Coxeter groups and their Schläfli symbols. It provides information on the order of the Coxeter groups, the Schläfli symbols that define each polytope, and counts of their facets, vertices, edges, faces and cells. The polytopes range from a line segment and pentagon to the dodecahedron, 120-cell, and a honeycomb of 120-cells.
Euler diagram for P, NP, NP-complete, and NP-hard set of problems
If there is a polynomial algorithm for any NP-hard problem, then there are polynomial algorithms for all problems in NP, and hence P = NP.
If P ≠ NP, then NP-hard problems cannot be solved in polynomial time, while P = NP does not resolve whether the NP-hard problems can be solved in polynomial time;
IEEE Certificate
Prof. C. Annamalai completed a course titled "System and User Space Virtualization Support in Yocto - the Yocto MetiVirtualization Project" on March 26, 2013 and earned 1 professional development hour.
NASA Certificate for My "Face in Space"
This certificate certifies that a face likeness of Chinnaraji Annamalai flew aboard the Space Shuttle Discovery on its STS-133 mission from February 24 to March 9, 2011. The face flew at an altitude of 220 miles above Earth and an orbital speed of over 17,400 miles per hour delivering supplies to the International Space Station. The NASA crew thanked Chinnaraji Annamalai for sharing in the excitement of the mission and exploration of space.
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Certificate on Computer Science, The Institute of Mathematical Sciences Chennai
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