How Do You Spell ABUNDANT NUMBER?

Pronunciation: [ɐbˈʌndənt nˈʌmbə] (IPA)

Abundant numbers are those integers whose sum of divisors is greater than twice the number itself. In IPA phonetic transcription, 'abundant' is pronounced as /əˈbʌndənt/. The word is spelled with a 'b' after the 'a' and before the 'u'. This is because the stressed syllable is 'bun', and the 'b' helps to create the correct sound. Additionally, the word contains an unstressed vowel sound represented by the schwa 'ə'. This sound is commonly used in English, especially for unstressed syllables, and represents a neutral, mid-central vowel.

ABUNDANT NUMBER Meaning and Definition

  1. An abundant number, in the domain of mathematics, refers to a positive integer that satisfies a particular set of conditions. More specifically, an abundant number is defined as a number where the sum of its proper divisors (which are all the divisors of the number excluding the number itself) is greater than the number itself. In other words, an abundant number is abundant in the sense that the sum of its divisors exceeds its value.

    For instance, let's consider the number 12. The divisors of 12 are 1, 2, 3, 4, 6, and 12. The proper divisors of 12 are 1, 2, 3, 4, and 6. The sum of these proper divisors is 1 + 2 + 3 + 4 + 6 = 16, which is greater than the number 12 itself. Hence, 12 is an abundant number.

    Abundant numbers are of interest in the field of number theory due to their unique properties and relationships with other types of numbers. They can be contrasted with deficient numbers (where the sum of the proper divisors is less than the number) and perfect numbers (where the sum of the proper divisors is equal to the number). Abundant numbers play a role in various mathematical concepts and problems, such as the study of amicable numbers, which are pairs of numbers where the sum of the proper divisors of each number is equal to the other number.

Etymology of ABUNDANT NUMBER

The word "abundant" in the term "abundant number" comes from the Latin word "abundans", which means "overflowing" or "excessive". This Latin word is derived from the verb "abundare", meaning "to overflow" or "to abound".

The term "abundant number" was first introduced in mathematics by Nicomachus of Gerasa, a Greek mathematician who lived in the 1st century AD. In his book "Introduction to Arithmetic", Nicomachus described abundant numbers as those numbers whose proper divisors (excluding the number itself) sum up to a larger value than the number itself. He used the term "abundant" because these numbers have an abundance of divisors compared to their value.