Showing posts with label calculus. Show all posts
Showing posts with label calculus. Show all posts

May 16 - Happy Birthday, Maria Gaetana Agnesi

 Posted on May 16, 2021


This is an update of my post published May 16, 2010:


Born on this day in 1718, in Milan, Italy, Maria Gaetana Agnesi is the first woman in the Western world considered to be an important mathematician since Ancient Greece's Hypatia, back in the 5th Century.

Agnesi was also a philosopher and a linguist.

Agnesi was a child prodigy. At 
age 9, she wrote a one-hour speech (in Latin) on the right of women to be educated, and she delivered it to an academic group.  By 13 she was considered a “Walking Polyglot” because she knew French, Greek, Hebrew, Spanish, German, Latin, and of course her native Italian. From age 15 to 20, her father organized meetings at their house: the most learned men in Bologna would come, and the teenage Agnesi would read and argue philosophical questions. However, she didn't really want to participate in these events, and at 20 she put a stop to them.
Google's celebration of Agnesi might look weird -
like, what's with the lines? - but the image harkens
back to one of Agnesi's diagrams:


Agnesi was considered dazzingly beautiful. She wanted to enter a convent and just study, but her father asked her to continue to teach her younger siblings. (Maria's mother had died, and her father married two more times.) All told, Maria was the oldest of her father's 21 children, so teaching all of them took a lot of her time.

Agnesi's biggest contribution to mathematics was a two-volume book on differential and integral calculus that brought together in a systematic way the work of several different mathematicians, with her own analysis and interpretations. When it was published in 1748, Analytical Institutions made an academic sensation.
Agnesi also became a university professor (Wikipedia claims she is the first woman university professor). She eventually joined a convent and helped the poor, homeless, and sick.

Agnesi wrote about calculus.
You may be thinking, “What is calculus, anyway?”


Watch this very short video to find out!



Play Around with Math!
This English version of a Dutch website has tons of really interesting math puzzles and games. I loved looking at the Impossible Object (rotate it around to see the illusion), and I played Colouring Sides 1 (fun!) and Falling Sums (also good).

Click Math Arcade on the FunBrain website for some math “video games.”




 

January 6 – Happy Birthday, Jacob Bernoulli

Posted on January 6, 2015

Jacob was one of eight gifted mathematicians in his family (and the first)! Born in Switzerland on this date in 1655, he so loved the logarithmic spiral, he asked that it be carved on his gravestone, which was erected after his 1705 death.

In between his birth and death, Jacob Bernoulli made many contributions to calculus, but he is most famous for his work on probability.

Here are some of the things that Bernoulli explored, discovered, and made contributions to:
You probably know that infinity is endless. Well, an infinite series is the sum of infinitely many numbers related to each other in a particular, defined way. Here is an example:

1/2 + 1/4 + 1/8 + 1/2^n

As n gets larger and larger, the fraction ½  to the nth power gets smaller and smaller, and although it seems that you can never QUITE get to the number 1, since there are an infinite number of fractions added to the series, we say that the answer converges on 1.

By the way, infinite series are important in practical fields such as engineering and biology!


This important number is approximately 2.71828 but it is irrational, so the digits after the decimal place go on and on and on and on...forever! Although it seems impossible that this number would be important in any way, Bernoulli discovered it when studying compounding interest (something that banks do so that you can grow your money!).






A differential equation states how a rate of change in one variable is related to other variables.


Probability is simply the likelihood of something happening. You can explore probability using dice, cards, spinners, or colored M&Ms. 

Here are some simple questions you can ask (there are way more complicated questions!):

  • If you throw one die ten times, what percent of the time will you roll a 6? How about if you throw the die ten thousand times?

  • In the game 21, if you have 11 points and want to get to 21, how likely are you to get 10 points in your next card? (Face cards AND the ten-spot cards are all worth 10 points.) Obviously, it depends on how many 10's have already been played!

  • If there are 30 spots on the spinner, alternating black and red, what is the likelihood of spinning a red?

  • What is the likelihood of pulling out a brown M&M from a full bag of M&Ms?

Here is a really interesting probability problem called the Monty Hall Problem.



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May 16, 2010


Happy Birthday, Maria Gaetana Agnesi
Born on this day in 1718, in Milan, Italy, Agnesi is the first woman in the Western world considered to be an important mathematician since Greece's Hypatia (5th Century). Agnesi was also a philosopher and a linguist.

Agnesi was a child prodigy, and by 13 she was a “Walking Polyglot” because she knew French, Greek, Hebrew, Spanish, German, Latin, and of course her native Italian. At age 9, she
wrote a one-hour speech (in Latin) on the right of women to be educated, and she delivered it to an academic group. From age 15 to 20, her father organized meetings at their house: the most learned men in Bologna would come, and the teenage Agnesi would read and argue philosophical questions. However, she didn't really want to participate in these events, and at 20 she put a stop to them.

Agnesi was considered dazzingly beautiful. She wanted to enter a convent and just stu
dy, but her father asked her to continue to teach her younger siblings. (Maria's mother had died, and her father married two more times.) All told, Maria was the oldest of her father's 21 children, so teaching all of them took a lot of her time.

Agnesi's biggest contribution to mathematics was a two-volume book on differential and integral calculus that brought together in a systematic way the work of several different mathematicians, with her own analysis and interpretations. When it was published in 1748, Analytical Institutions made an academic sensation.
Agnesi also became a university professor (Wikipedia claims she is the first woman university professor) and eventually joined a convent and helped the poor, homeless, and sick.
Agnesi wrote about calculus.
You may be thinking, “What is calculus, anyway?”


Watch this very short video to find out!


Play Around with Math!


  • This English version of a Dutch website has tons of really interesting math puzzles and games. I loved looking at the Impossible Object (rotate it around to see the illusion), and I played Colouring Sides 1 (fun!) and Falling Sums (also good).

  • Math Galaxy has a “demo mode” that it offers for free. I tried a pretty challenging game called Bridge the Swamp.

  • Click Math Arcade on the FunBrain website for some math “video games.”