Vocabulary
Academic Word List
- real number
- whole number
- paradox
- hydrodynamic
- congruent
- electromagnetic
- fourth dimension
- quantum
- diagonal
- theorem
- axiom
- correspondence
Other Vocabulary
- atomic
- random
- decompose
- finite
- colonize
- equator
- parallel
- element
- hormones
- nurture
- radius
- regenerate
- feedback
Exercise
Please click the Exercise link to continue and do Exercises 1 and 2.
Pre-Listening
Use the questions to begin a discussion. Try to be sure everyone in your group gives their opinion and explains why they hold that opinion before moving on to the next question.
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What is a paradox?
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What kinds of paradox exist in STEM? How about in your personal life?
Exercise
Please click the Exercise link to continue and do Exercise 3.
Listening
Exercise
Listen to to the first 60 seconds of the video. In your group, discuss how this relates to the research you've just done and predict what you believe the rest of the Listening will be about and some of the topics that might be discussed. Try to identify the main idea of the video and note key information that you believe will be important to summarize the information. Try to rephrase vocabulary as much as possible.
Now listen to the complete video and take notes on it. When it is finished, talk to your group about the main ideas that are discussed in the Listening. In the box below, re-write the the predictions you made above by adding some more information from the Listening.
References
Banach-Tarski on wikipedia: https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox
Banach-Tarski proofs: http://math.uchicago.edu/~may/REU2014/REUPapers/Robinson.pdfhttps://www.math.hmc.edu/~su/papers.d...
https://www.math.hmc.edu/~su/papers.dir/banachtarski.pdf
Post-Listening
Exercise
Please click the Exercise link to continue and do exercises 6, 7 and 8.