verifying algebraic identity (a+b)^2 by activity method
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This activity aims to verify the algebraic formula (a + b)2 = a2 + 2ab + b2 through a hands-on activity using four colored pieces. The activity involves joining the four pieces together according to the procedure to demonstrate the expansion of the squared binomial. Upon completion, the activity confirms the algebraic formula through a visual representation.
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This document defines a perfect number as a number where the sum of all its factors (excluding the number itself) equals the number. It provides 6 and 28 as examples of perfect numbers. It then explains a method for finding perfect numbers by taking the product of (2p-1) and 2p-1, where p is a prime number, and lists the first 3 perfect numbers found using this method: 6, 28, and 496. It challenges the reader to find the next perfect number and first 10 perfect numbers using this method.
Number system, natural numbers to real numbers
Early humans developed systems for counting and keeping track of their animals. They realized counting could be represented through symbols like stones corresponding to each animal. This led to the development of early number systems. Over time, the number system evolved to include more complex concepts like zero, negative numbers, fractions, and irrational numbers to represent real-world situations. Key developments included the introduction of zero by the mathematician Aryabhata to represent nothing, the concept of positive and negative numbers from credit and debt in bartering systems, and the recognition of fractions and irrational numbers from sharing situations. Together, rational and irrational numbers make up the set of real numbers that can be used to represent all quantities in mathematics.
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