When is a billion not a billion?
Did you know that the American system for naming large numbers is not the same as the British system? What we call a billion, they call a thousand million. And what they call a billion, we call a trillion! And it continues from there. After a million, we do not agree on any of the names for large numbers. The chart below summarizes the differences. Number
As you can see, Americans name their numbers based on powers of 10 that are multiples of 3, while the British name theirs based on multiples of 6. The implicit curve equation(x2+y2-1)3-x2y3=0 produces the heart shape.
The sum of the digits of a number which is a multiple of 9 is always 9, i 45 : 4+5 = 9
1980 : 1+9+8+0=18 : 1+8 = 9
214164 : 2+1+4+1+6+4=18 : 1+8 = 9
142857 is a cyclic number, i.e., its digits are rotated around when multiplied by any number from 1 to 6. Like this: 142857 × 1 = 142857
142857 × 5 = 7 14285
142857 × 4 = 57 1428
142857 × 6 = 857 142
142857 × 2 = 2857 14
142857 × 3 = 42857 1
Mathematics is the abstract study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. THE EVOLUTION OF MATHEMATICS:
The evolution of mathematics might be seen as an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction, which is shared by many animals, was probably that of numbers: the realization that a collection of two apples and a collection of two oranges (for example) have something in common, namely quantity of their members. Evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have also recognized how to count abstract quantities, like time – days, seasons, years. More complex mathematics did not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic, algebra and geometry for taxation and other financial calculations, for building and construction, and for astronomy. The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns and the recording of time. In Babylonian mathematics elementary arithmetic(addition, subtraction, multiplication and division) first appears in the archaeological record .Numeracy pre-dated writing and numeral systems have been many and diverse, with the first known written numerals created by Egyptians in Middle Kingdom texts such as the Rhind Mathematical Papyrus. Between 600 and 300 BC the Ancient Greeks began a systematic study of mathematics in its own right with Greek mathematics. Mathematics has since been greatly extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today. According to Mikhail B. Sevryuk, in the...
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