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Which culture was the first to use integers?
The concept of integers, including positive and negative whole numbers, originated in ancient Mesopotamia around 3000 BCE. The Sumerians developed a system of counting using tokens to represent quantities, which eventually evolved into a written numerical system using cuneiform symbols. These early civilizations laid the foundation for the development of integers as a fundamental mathematical concept.
Integers you use in everyday life?
I presume you're talking in particular about places where we use numbers that may be either positive or negative, and it's really helpful to be able to treat them as the same kind of number, instead of needing a separate rule for each combination of negative and positive numbers. Some examples aren't really integers but positive or negative real numbers. How about temperatures? Conversion between Fahrenheit and Celsius on a sub-freezing day is a good exercise in using negative numbers. Elevations go negative in places like Death Valley and the Dead Sea. Comparing the base-to-peak heights of Mount Everest and Mauna Loa is an exercise in subtracting negative numbers. Latitude and longitude are easier to work with if you take east/north as positive and west/south as negative. The most obviously useful calculation here is in working with time zones - you'll find charts with time zones labeled EST = -5, Eastern Europe = +2, etc. Years are a peculiar case. AD and BC were invented around AD 525, before negative numbers (or zero) were really understood, so there was no year zero. The year after 1 BC was AD 1. If it had been done right, we would have been able to compute the years between 43 BC and 33 AD as 33 - (-43) = 76. But because dates aren't integers, you have to say 33 + 43 - 1 = 75. In other words, when the calendar was devised, people just accepted the need for special cases, but with the invention of integers, we found a better way. By the way, the federal government does not assume that taxpayers understand integers, so the 104 form uses the special-case approach: "If line 64 is LESS than line 59, subtract line 64 from line 59 and write it in line 65. If line 64 is GREATER than line 59, subtract line 59 from line 64 and write it in line 66." (That's the idea anyway, I got my form yesterday but I don't have it in front of me.) I can't think of any everyday cases where we multiply negatives by negatives. But when your students learn about quadratic equations, they will be benefiting again from the no-special-cases property of integers. Early developers of algebra had to present solutions for 6 kinds of quadratic equations: Money can also be used as an integer because when you think about it as its in piggy bank going in and out of it, it makes you think about it.
Why are square numbers important?
The pattern and application of squaring numbers is deeply inherent in the way nature and the universe express themselves. God's design, if you will. Early Mathematicians didn't create the application of squaring numbers, they observed it in nature. Isaac Newton observed that a falling object on Earth travels 16 feet multiplied by the square of the time, I.e. If an object falls for 2 seconds then, 16x2x2=64 feet. Cause that's the way nature intended : )
What is the Gaussian method of counting consecutive numbers?
This is attributed to an early school lesson when the teacher thought he would keep the class busy whilst he popped out for something. He set the test of adding all the whole numbers from 1-100. By the time he reached the door, Gauss had the answer. Gauss imagined the problem as 1 + 2 + 3 +........+98 + 99 + 100, but then he wrote the numbers underneath but in reverse order. 100 +99 + 98..........+3 + 2 + 1 So each 100 pairs of vertical numbers added up to 101 so the total was 10100 but this is twice the true answer as each number is included twice. The total is therefore 5050. This lead to the general formula that the sum of consecutive numbers from 1 to n is n(n+ 1) ÷ 2.
What numbers go into 675?
idfk ok so get to school early in da moring a ask ur god damm teacher n pay attention in class u dnt learn dat way :|
