Showing posts with label mathematics. Show all posts
Showing posts with label mathematics. Show all posts

Wednesday, August 17, 2022

Mathematician Pierre de Fermat and his Enigma on This Day in History


This Day In History: Mathematician Pierre de Fermat was born on this day in 1607. He is best known for his famous Last Theorem (aka Fermat's conjecture), a math problem that was finally solved after 358 years by Andrew Wiles in 1994. It took Wiles 30 years, and a lot of that time was spent in self-imposed solitary confinement to solve this problem. 

Fermat's theorem stimulated the development of algebraic number theory in the 19th and 20th centuries. It is among the most notable theorems in the history of mathematics and prior to its proof was in the Guinness Book of World Records as the "most difficult mathematical problem", in part because the theorem has the largest number of unsuccessful proofs.

Simon Singh's book about Fermat’s Last Theorem became the first book about mathematics to become a No.1 bestseller...and yes, it was a really good book.

The History and Mystery of Alchemy is now available on Amazon...and it is only 99 cents.

Monday, March 14, 2022

March 14 is Pi Day (3.14)


This Day in History: Today is Pi Day (3.14). Also known as "Archimedes' constant" Pi also has an entire language made from the number it. In “Pi-lish” the first word has three letters, the second word has one letter, the third has four letters, and so on. There is an entire book, called "Not a Wake" written in this language. 

Givenchy sells a men’s cologne with the name ‘Pi,’ Kate Bush has a song called Pi where she actually recites Pi and there is a late 90's movie called Pi that was weird and at the same time rather interesting. Oh, and Albert Einstein was born on Pi day (1879) and Stephen Hawking died on Pi day (2018).


Many have tried to memorize the many digits of Pi (3.14159…). The record for the most digits of Pi memorized belongs to Chao Lu, of China, who recited Pi from memory to 67,890 places in 2005, according to The Guinness World Records. Computers can get even more accurate measurements. As of December 2013, computers calculated Pi to a record 12 trillion digits.


The History of Pi, by Marie Gugle 1920
It was not until the middle of the eighteenth century that the Greek letter (PI) came into use as a symbol for the ratio of the circumference to the diameter of a circle. But from earliest times mathematicians knew that there was such a constant ratio. Different values were given it in different periods of history.

1. One of the earliest books we have is the Ahmes (Ah'mez) Papyrus, written about 1700 B.c. In this manuscript a value is given to PI equal to 256/81 or 3.1604.

2. The Jews and Babylonians considered PI equal to 3. This fact is shown in the measures given for sacred vessels in I Kings vii, 23 and II Chronicles iv, 2.

3. Archimedes of Syracuse, who lived between 287 and 212 B.c, was a great mechanical genius as well as mathematician. You will find it interesting to read the stories of his detection of the fraudulent goldsmith; his use of burning glasses to destroy the Roman ships; his apparatus for launching ships; and the Archimedean screw used to drain the flooded fields of Egypt.

Archimedes proved that the value of PI is between 3 1/7 and 3 10/71.

We can understand these values better by putting them in decimal form, but Archimedes did not have this advantage, because no one knew anything about decimal fractions until nearly 1600 A.d.

4. Ptolemy, a great astronomer of Alexandria about 150 A.d., used 3 17/120 as the value of PI. As a decimal 3 17/120 = 3.14166.
5. Between 400 and 600 A.d. the Hindus used PI = 3 or 3 1/8 and PI = which is 3.1622.

The Chinese had used PI = about 200 A.d.


6. The exact value of PI cannot be expressed in ordinary figures, although many persons have contended long and earnestly that it could be done. If this were possible, a square could be constructed exactly equal to a circle. These people are known as "circle-squarers."

About 1600 the value of PI was calculated to 35 decimal places. Since then it has been calculated to 707 decimal places, but it will never come out "even." In other words no square can be constructed that is exactly equal to a circle.

The value correct to the first 35 places is as follows:

PI = 3.14159265358979323846246338327905288 When very exact measures are needed, we use 7r = 3.14159 or 3.1416.

For less exact measures, we use PI = 3.14 or PI = 3 1/7.

For a list of all of my disks and ebooks (Amazon and PDF) click here

Tuesday, November 23, 2021

The Fibonacci Sequence of Numbers on This Day in History

 

Fibonacci and the Stock Market

Today in History: Today is Fibonacci Day. A Fibonacci sequence is a series of numbers where a number is the sum of the two numbers before it. For example: 1, 1, 2, 3...is a Fibonacci sequence. Here, 2 is the sum of the two numbers before it (1+1). Similarly, 3 is the sum of the two numbers before it (1+2). November 23 is celebrated as Fibonacci day because when the date is written in the mm/dd format (11/23), the digits in the date form a Fibonacci sequence: 1,1,2,3. https://www.timeanddate.com/holidays/fun/fibonacci-day

Fibonacci, also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ('Leonardo the Traveller from Pisa'), was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages".

Fibonacci popularized the Hindu–Arabic numeral system in the Western world primarily through his composition in 1202 of Liber Abaci (Book of Calculation).He also introduced Europe to the sequence of Fibonacci numbers, which he used as an example in Liber Abaci. Liber Abaci posed and solved a problem involving the growth of a population of rabbits based on idealized assumptions. The solution, generation by generation, was a sequence of numbers later known as Fibonacci numbers.

The Fibonacci sequence pops up in everything from nature to music to computer science to the stock market.

Mozart used the Fibonacci in his Sonata 279. In fact, he wrote the mathematical equations in the margins in the sheet music. 


You can also use the Fibonacci numbers to do conversion. "Fibonacci numbers can be used to approximately convert from miles to kilometers and back. Here is how. Take two consecutive Fibonacci numbers, for example 5 and 8. And you're done converting. No kidding – there are 8 kilometers in 5 miles. To convert back just read the result from the other end – there are 5 miles in 8 km! Another example. Let's take two consecutive Fibonacci numbers 21 and 34. What this tells us is that there are approximately 34 km in 21 miles and vice versa." Source

I came across this interesting comment on Youtube:

"1,1,2,3,5,8,13,21,34,55,89,144... (...233.377.610...)

- I was noticing a while back that 144 is the 12th # in the sequence...

- 12 is also its root

- &if you take 144's mirror-441, it's root is 21, the mirror of 12 who's square is 144

- same thing with 13 (13x13=169 31x31=961)

(I haven't bothered to check how many more numbers might do that but I notice that not all do, so that' is kind of interesting but I don't know if its profound or significant) or if I should see it as pointing toward something else.

Also, this could be meaningless or just coincidence... but I was also recalling how I read that the Mayan's use 144,000 (144,000 days in a Baktun) and also 144,000 is used in the Christian Bible too. Maybe someone has some thoughts on this too.

Also, the divine number is neat in the way in which if you square 1.618 [Golden Ratio] it will be roughly the same as if you added 1.0 to it. Kind of weird." 

See also: Fibonacci Number Patterns

See also Fun with Mathematics - Over 250 PDF Books on DVDrom