Archimedes was born in the year 287 BCE. at a city known as Syracuse. His father was a man named Phidias who was an astronomer. At one point one of Archimedes friends, known as Heraclides, wrote a biography of his life, but was lost and never recovered. We know very little of his life, whether he had a wife or children. He died in 212 BCE during The Punic War. He was killed by a Roman Soldier in the conquest of Syracuse.
There are a plethora of things he gave to the human race. For example . Everyone uses at least once in there life. The way he did it is amazing. Remember he did not have any form of a calculator so he had to use pure brain power. He first imagined a circle, plain and simple. He then put two equilateral triangles on the inside and outside which were easy to find the perimeter. Now he knew that the circumference of the circle was between the smaller triangle inside the circle and the larger on the outside of the circle. He kept adding to this and slowly, but surely got to the 90-sided polygon.
“Is this a circle or polygon?”
This is the 90-sided one, but he actually used the 96-sided polygon. This is just an example of how similar it looks to a circle with the human eye. Like I said he used the 96-sided polygon which Archimedes found that π was greater than the fraction 25344/8069, and less than the fraction 29376/9347. Just a reminder, he had no calculator to do this for him only his massive brain. Now this is a big number division so he went and simplified it and came up with π was bigger than 3 and 1/7 and smaller than 3 and 10/71.
Another thing he did is come up with the Beast Number. Here’s the story, Archimedes became very annoyed with people telling him he could not tell how many particles of sand there were on a beach. So he went to prove them wrong. A cool thing about this story is that when Archie was doing these things the biggest number was 10,000 which was known as a myriad. WE could also state this number as 10^4. Well this was not big enough to state the number of sands on a beach so he came up with 10^8 or a myriad’s myriad or 10,000 x 10,000. Thus creating the hugely popular exponents. So over time he came up with this number.
It’s one followed by 80 quadrillion zeros the example I have there is 205 zeros so just think about that for a second. Now I am going to hurt your head. That number is not even close to infinity. If you think it is closer than 100 or 10, maybe even 1 you are incorrect because infinity is not touchable not matter how large the number is.
We all think of infinity as super humongous, right? While that can be true it can be extremely small so we call it endless instead. If there is no reason for something to stop then it is known as infinet. This does not mean it is growing either it is just saying infinity is every number at once. To explain, infinity does not do, but just is.
Since we are talking about infinity lets talk a little bit about limits. What is a limit? Well a limit is a number or thing that something can not touch. For example this graph y = 1/x.
Anything added or subtracted or added to infinity x= where x is a real number. One of the most important things to know about infinity is that -x where x is a real number. What that equation says is that minus infinity is equal to or greater than any real number and any real number is equal to or less than infinity.
Properties of Infinity
∞ + ∞ = ∞ For x>0 : For x<0 :
-∞ + -∞ = -∞ |x + ∞ = ∞ |x - ∞ = -∞
∞ × ∞ = ∞ |x - (-∞) = ∞ |x + (-∞) = -∞
-∞ × -∞ = ∞ |x × ∞ = ∞ |x × ∞ = -∞
-∞ × ∞ = -∞ |x × (-∞) = -∞ |x × (-∞) = ∞
0 × ∞ |∞^0 |∞ / ∞
0 × -∞ |∞ - ∞ |1∞
Wouldn’t ∞ / ∞ equal 1?
Because infinity = any real number ∞ / ∞ = 2∞ / ∞ which means that: 1/1 = 2/1 which is not true.
Wouldn’t ∞ - ∞ equal zero?
∞-∞ can equal zero, but it can also be seen like this 3∞ - 2∞ which equals ∞ not zero. Because of that it is “undefined”.
Why is 1∞ “undefined”?
1∞ is “undefined” because it equals 10, but it also equals 10,000,000,000,000,000,000. Yes that is a lot of zeros. I don’t even know what that number is called.