4 out of 4 stars
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The Fundamental Principle of Digits of a Number, written by Chibamba Mulenga, PhD, is a mathematical treatise outlining numerical concepts discovered by the author relating to the digits of numbers. The basic premise is that if the digits of any number are rearranged and one of the two permutations is subtracted from the other, the difference between them is always a multiple of nine. For example, the digits of the number 938 can be rearranged to form the number 983; the difference between these is 45, which is a multiple of nine. The same digits can also be rearranged to form the number 839; the difference between 938 and 839 is 99, which is also a multiple of nine. In this book, Mulenga proves that this principle holds for all integers; from here, he expands into increasingly complex theoretical manipulations, building on his early discoveries.
Perhaps you learned in school, as I did, that a number can be quickly recognized as a multiple of nine if the sum of its digits is also a multiple of nine; for example, we know immediately that 351 is evenly divisible by nine because the sum of three, five, and one is nine. Few if any of us, though, have seriously thought about why this might be the case or what else it may imply. Mulenga expands on the concept and advances it beyond what I would have guessed was possible. As a doctoral mathematician, the author defines his terms meticulously and extensively tests his theorems, allowing the development of airtight conclusions. I greatly appreciated this level of precision and attention to fine detail.
No mathematic training higher than algebra is required to follow the progression of discoveries, tests, and further discoveries. However, the subject matter tends to make for dry reading. Readers who are keenly interested in mathematics will enjoy delving into the fine distinctions between terms, but more casual readers may find themselves bogged down in the minutiae. It is also somewhat challenging to find ways to apply the content of the book to one’s everyday life. Therefore, the ideal reader is one who enjoys reading about mathematics purely as a conceptual exercise rather than for a real-world purpose.
The book appears polished, with only two tiny mistakes in the text. As you might expect, there is no objectionable content, but I still could only recommend the book for adults because the subject matter would likely baffle any youth who wasn’t an extreme mathematical prodigy.
The Fundamental Principle of Digits of a Number earns a score of 4 out of 4 for its imaginative investigation of a concept that has until now escaped recognition despite being right before our eyes all along. I almost removed one star for the density of the content, but because I believe that it is a result of the subject matter rather than the writing, I cannot fault the author. The book would most appeal to lovers of mathematics looking for a conceptual, thought-provoking read.
The Fundamental Principle of Digits of a Number
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