nPostednon January 6, 2015
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Jacobnwas one of eight gifted mathematicians in his family (and the first)!nBorn in Switzerland on this date in 1655, he so loved the logarithmicnspiral, he asked that it be carved on his gravestone, which wasnerected after his 1705 death.
Jacobnwas one of eight gifted mathematicians in his family (and the first)!nBorn in Switzerland on this date in 1655, he so loved the logarithmicnspiral, he asked that it be carved on his gravestone, which wasnerected after his 1705 death.n
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nInnbetween his birth and death, Jacob Bernoulli made many contributionsnto calculus, but he is most famous for his work on probability.
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nHerenare some of the things that Bernoulli explored, discovered, and madencontributions to:
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You probably know thatninfinity is endless. Well, an infinite series is the sum ofninfinitely many numbers related to each other in a particular,ndefined way. Here is an example:
You probably know thatninfinity is endless. Well, an infinite series is the sum ofninfinitely many numbers related to each other in a particular,ndefined way. Here is an example:n
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1/2 + 1/4 + 1/8 + 1/2^n
1/2 + 1/4 + 1/8 + 1/2^n
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nAs n gets larger andnlarger, the fraction ½ to the nth power gets smaller and smaller, and although itnseems that you can never QUITE get to the number 1, since there arenan infinite number of fractions added to the series, we say that thenanswer converges on 1.
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nBy the way, infinitenseries are important in practical fields such as engineering andnbiology!
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nThe mathematical constant e
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This important number isnapproximately 2.71828 but it is irrational, so the digits after thendecimal place go on and on and on and on…forever! Although it seemsnimpossible that this number would be important in any way, Bernoullindiscovered it when studying compounding interest (something thatnbanks do so that you can grow your money!).
This important number isnapproximately 2.71828 but it is irrational, so the digits after thendecimal place go on and on and on and on…forever! Although it seemsnimpossible that this number would be important in any way, Bernoullindiscovered it when studying compounding interest (something thatnbanks do so that you can grow your money!).n
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nA differential equationnstates how a rate of change in one variable is related to othernvariables. n
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Probability is simply thenlikelihood of something happening. You can explore probability usingndice, cards, spinners, or colored M&Ms.
Probability is simply thenlikelihood of something happening. You can explore probability usingndice, cards, spinners, or colored M&Ms. n
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nHere are some simplenquestions you can ask (there are way more complicated questions!):
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- If you throw one die tenntimes, what percent of the time will you roll a 6? How about if younthrow the die ten thousand times?
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- In the game 21, if younhave 11 points and want to get to 21, how likely are you to get 10npoints in your next card? (Face cards AND the ten-spot cards are allnworth 10 points.) Obviously, it depends on how many 10’s have alreadynbeen played!
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- If there are 30 spots onnthe spinner, alternating black and red, what is the likelihood ofnspinning a red?
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- What is the likelihood ofnpulling out a brown M&M from a full bag of M&Ms?
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Here is a reallyninteresting probability problem called the Monty Hall Problem.
Here is a reallyninteresting probability problem called the Monty Hall Problem.n
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nAlsonon this date:
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Archeologist Heinrich Schliemann’s birthday
Archeologist Heinrich Schliemann’s birthday n
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nBirthdaynof French heroine Joan of Arc
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nCommunicationsnInventions Day
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nThreenKings Day / Epiphany / Twelfth Night
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nAnniversarynof opening of first Montessori school
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nPlannahead:
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nChecknout my Pinterest pages on:
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nJanuaryn birthdays
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nHistoricaln anniversaries in January
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nAndnhere are my Pinterest boards for:
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nFebruaryn holidays
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nFebruaryn birthdays
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