After Quiz Activities
I will use this page to have students investigate future or past topics after quizzes. Use this time to explore for yourself, find cool and interesting tidbits and just become a curious learner.
After 1.1-2.2 Quiz
Mathematics of Love TED Talk
In the spirit of Valentine's Day, watch the TED talk supplied below (I have about 4 or 5 headphones to borrow in class, otherwise use your own or turn on subtitles by clicking on the CC button in the lower right portion of the video). As you watch, write your answers to the following questions:
1) Whose distribution of scores was left-skewed and whose was bimodal between Portia de Rossi and Sarah Jessica Parker?
2) What is Hannah's tip #2?
3) What are the two ways that Hannah's tip #2 could fail?
4) In Hannah's tip #3, she uses mathematics and a psychologist's study to show that most successful relationships occur not with a high negativity threshold but a low one. What did she explain a low negativity threshold implied?
1) Whose distribution of scores was left-skewed and whose was bimodal between Portia de Rossi and Sarah Jessica Parker?
2) What is Hannah's tip #2?
3) What are the two ways that Hannah's tip #2 could fail?
4) In Hannah's tip #3, she uses mathematics and a psychologist's study to show that most successful relationships occur not with a high negativity threshold but a low one. What did she explain a low negativity threshold implied?
After 3.1 - 3.4 Quiz
A Story from the History of Math
Path of Shortest Descent: The Brachistochrone
The story of the brachistochrone begins in 1696. The Swiss mathematician Johann Bernoulli (for those in Calculus, he is the mathematician who tutored l'Hopital and from whom l'Hopital stole the famous rule used to evaluate limits) challenged the world to solve a simply stated problem:
"find the path that allows a ball to move down a ramp in the shortest amount of time."
Most believe it to be a straight line, but you may be surprised by the solution.
"find the path that allows a ball to move down a ramp in the shortest amount of time."
Most believe it to be a straight line, but you may be surprised by the solution.
Johann pulbished his challenge in a journal that read:
"I, Johann Bernoulli, address the most brilliant mathematicians in the world. Nothing is more attractive to intelligent people than an honest, challenging problem, whose possible solution will bestow fame and remain as a lasting monument. Following the example set by Pascal, Fermat, etc., I hope to gain the gratitude of the whole scientific community by placing before the finest mathematicians of our time a problem which will test their methods and the strength of their intellect. If someone communicates to me the solution of the proposed problem, I shall publicly declare him worthy of praise."
Bernoulli allowed six months for the solutions, but none were received during this period. At the request of another mathematician, the time was publicly extended for a year and a half. On January 29, 1697 the challenge was received by Isaac Newton, who found it in his mail, in a letter directly from Johann Bernoulli, when he arrived home from the Royal Mint at 4 p.m. He stayed up all night to solve it and mailed the solution anonymously by the next post. Upon reading the solution, Bernoulli immediately recognized its author, exclaiming that he recognizes a "lion from his claw mark." This story gives some idea of Newton's power, since Johann Bernoulli himself took two weeks to solve it. Newton also wrote, "I do not love to be dunned [pestered] and teased by foreigners about mathematical things."
Now, watch the video below concerning the brachistochrone in real life and then answer the questions below the video. (I have about 4 or 5 headphones to borrow in class above the calculators, otherwise use your own or turn on subtitles by clicking on the CC button in the lower right portion of the video)
"I, Johann Bernoulli, address the most brilliant mathematicians in the world. Nothing is more attractive to intelligent people than an honest, challenging problem, whose possible solution will bestow fame and remain as a lasting monument. Following the example set by Pascal, Fermat, etc., I hope to gain the gratitude of the whole scientific community by placing before the finest mathematicians of our time a problem which will test their methods and the strength of their intellect. If someone communicates to me the solution of the proposed problem, I shall publicly declare him worthy of praise."
Bernoulli allowed six months for the solutions, but none were received during this period. At the request of another mathematician, the time was publicly extended for a year and a half. On January 29, 1697 the challenge was received by Isaac Newton, who found it in his mail, in a letter directly from Johann Bernoulli, when he arrived home from the Royal Mint at 4 p.m. He stayed up all night to solve it and mailed the solution anonymously by the next post. Upon reading the solution, Bernoulli immediately recognized its author, exclaiming that he recognizes a "lion from his claw mark." This story gives some idea of Newton's power, since Johann Bernoulli himself took two weeks to solve it. Newton also wrote, "I do not love to be dunned [pestered] and teased by foreigners about mathematical things."
Now, watch the video below concerning the brachistochrone in real life and then answer the questions below the video. (I have about 4 or 5 headphones to borrow in class above the calculators, otherwise use your own or turn on subtitles by clicking on the CC button in the lower right portion of the video)
Questions for Brachistochrone Video (watch from 16:43 to 24:15):
1) The shortest distance (a straight line) produces the fastest or slowest path?
2) Qualitatively, the brachistrochrone is the fastest because it balances which two aspects of the movement?
3) What does tautochrone mean?
4) A brachistochrone is also a tautochrone, which means what in terms of where you drop the ball on the ramp and the time it takes to get to the bottom?
1) The shortest distance (a straight line) produces the fastest or slowest path?
2) Qualitatively, the brachistrochrone is the fastest because it balances which two aspects of the movement?
3) What does tautochrone mean?
4) A brachistochrone is also a tautochrone, which means what in terms of where you drop the ball on the ramp and the time it takes to get to the bottom?
After 4.1-4.3 Quiz
Read the tweet below. Then click on the green survey link to submit your response to the survey question.
SURVEY LINK
SURVEY LINK
After 5.1 - 5.3 Quiz
Watch video and write two-sentence summary at the bottom of your most recent HW assignment. (I have about 4 or 5 headphones to borrow in class above the calculators, otherwise use your own or turn on subtitles by clicking on the CC button in the lower right portion of the video)