Number treasury 2: a collection of facts and conjectures, problems and investigations, about more than one hundred kinds of numbers
Grades: 7 8 9 10 11 12
ENC#: ENC-024926
Publisher: Dale Seymour Publications
Date: 2001
Ordering Information
|
|
Subjects:
 | Mathematics
Famous problems. History. Mathematicians. Number theory. |
Resource Type:
Lessons and activities; Study guides and tutorials.
Abstract:
This book on number theory, for grades 7 through 12, contains activities for students and is a resource for teachers. The book offers 28 student investigations that present a certain fact or algorithm and prompt students to explore the topic further, including researching and writing a report about a particular mathematician. For teachers, the book provides number theory facts, examples, and exercises that supplement instruction and provide additional information. One student investigation on highly composite numbers gives students the definition of highly composite numbers, a brief biography of Srinivasa Ramanujan, and examples of how to tell if a number falls into this category. Students then generate of list of highly composite numbers, perform several related operations, and write a report on the life and work of Ramanujan. (Author/SB)
Table of Contents:
Foreword
1. Investigations
2. Numbers based on divisors and proper divisors
Positive integers
Divisors, multiples, proper divisors
Prime and composite numbers
Sieve of Eratosthenes
Prime factorization property (fundamental theorem of arithmetic)
Testing for primes
Divisors of an integer, GCD and LCM
Relatively prime and euler numbers
Abundant, deficient, and perfect numbers
Sums and differences of abundant and deficient numbers
Products of abundant and deficient numbers
Multiples of perfect numbers
Consecutive integers and abundant numbers
Abundant numbers as sums of abundant numbers
Powers of primes and deficient numbers
Even and odd integers, even perfect numbers, and mersenne primes
Multiply perfect numbers
Almost perfect numbers
Semiperfect numbers
Weird abundant numbers
Operations on semiperfect numbers
Primitive semiperfect numbers
Unitary numbers
Amicable numbers
Imperfectly amicable numbers
Sociable numbers and crowds
Practical numbers
Baselike numbers
3. Plane figurate numbers
Polygons
Figurate numbers
Triangular numbers
Operations on triangular numbers
Perfect numbers, triangular numbers, and sums of cubes
Pascal's triangle
Triangle inequality numbers
Rectangular numbers
Square numbers
Sums of square numbers
Positive square pair numbers
Bigrade numbers
Pythagorean triples
Primitive Pythagorean triples
Congruent numbers
Fermat's last theorem
Happy numbers
Operations on happy numbers
Happy number words
Repeating cycles
Patterns in squares of 1, 11, 111
Squarefree numbers
Tetragonal numbers
Pentagonal numbers
Hexagonal numbers
Recursion and figurate numbers
Remainder patterns in figurate numbers
Gnomic numbers
Male and female numbers
Lo-Shu magic square
4. Solid figurate numbers
Polyhedra, solid figurate numbers
Pyramidal numbers
Tetrahedral numbers and triangular pyramidal numbers
Square pyramidal numbers
Pentagonal pyramidal numbers
Hexagonal pyramidal numbers
Heptagonal and octagonal pyramidal numbers
Star numbers and star pyramidal numbers
Rectangular pyramidal numbers
Cubic numbers
Integers as sums and differences of cubic numbers, 1729
Pythagorean parallelepiped numbers
Circular and spherical numbers
5. More prime connections
Goldbach's conjectures
Integers as sums of odd integers
Integers as sums of two composite numbers
Positive prime pair numbers
Prime line and prime circle numbers
Beprisque numbers
A primes between property
Germain primes
Twin primes
Semiprimes and boolean integers
Snowball primes
Lucky numbers
Prime and lucky numbers
Polya's conjecture on odd and even-type integers
Balanced numbers
Fermat numbers
Cullen numbers
Aaron numbers
6. Digital patterns and noteworthy numbers
Monodigit and repunit numbers and Langford sequences
Social and lonely numbers
Additive multidigital numbers
Multiplicative multidigital numbers
Kaprekar's number, 6174 and 99 and 1089
Doubling numbers
Good numbers
Nearly good semiperfect numbers
Powerful numbers
Armstrong numbers and digital invariant numbers
Narcissistic numbers
Additive digital root numbers
Additive persistence of integers
Multiplicative digital root numbers
Multiplicative persistence of integers
Modest, extremely modest numbers
Visible factor numbers
Nude numbers
7. More patterns and other interesting numbers
More sumes of consecutive integers
Product patterns for consecutive integers
Consecutive integer divisors
Consecutive number sums and square numbers
Factorial numbers, applications and extensions
Factorial sum numbers and subfactorial numbers
S.M. Ulam numbers and hailstone numbers
Palindromic numbers
Creating palindromic numbers
Palindromic number words and curiosities
Palindromic numbers and figurate numbers
Palindromic primes and emirps
Honest numbers
Bell numbers
Catalan numbers
Fibonacci numbers
Lucas numbers
Tribonacci numbers
Tetranacci numbers
Phibonacci numbers
Survivor numbers
Tautonymic numbers
Lagado numbers
Recommended readings
Glossary of numbers
Solutions to investigations
Solutions to exercises
Hints for solving extensions
Index
Vendor:
Dale Seymour Publications
Pearson Learning Group
PO Box 2500
Lebanon IN 46052
(800) 237-3142
(800) 321-3106
Fax: (800) 393-3156
http://www.pearsonlearning.com
|  |  |
Pricing Information:
| Description: 1 text (paperback) | Cost: $21.95 | ISBN: 978-0-7690-0011-4 | |
Publisher:
Dale Seymour Publications Contributor(s):
| Authors: Stanley J Bezuszka; Margaret J Kenney. |
Specifications:
1 text (303 pages : illustrations ; 28 cm.)
Record Created: 07/17/2002 Last Modified: 04/18/2005
| 
