Mathematician Richard Canary of the University of Michigan studies hyperbolic space, a world where curved lines are really straight and parallel. Imagine trying to hit a golf ball into a hole under such conditions! In this Hangout, Canary—a Sigma Xi Distinguished Lecturer—speaks with managing editor Fenella Saunders about hyperbolic space, drawing on examples from sports to explain the mind-twisting math.

A Storify of the Tweets detailing the discussion is shown below.

Playing Sports in Hyperbolic Space

University of Michigan mathematician Richard Canary studies a world where curved lies are really straight and parallel. Imagine trying to hit a golf ball into a hole under such conditions! Canary, a Sigma Xi Distinguished Lecturer, draws on examples from sports to explain the mind-twisting math.

1. 

   SigmaXiSociety@SigmaXiSociety

   Google Hangout today about #math, particularly hyperbolic space, featuring a Sigma Xi Distinguished Lecturer  https://twitter.com/AmSciMag/status/701888004537896961 …

   @JLVernonPhD

   ·

   Tue, Feb 23 2016 15:15:41

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2. 

   We're live: Hangout on hyperbolic geometry ft @UMich #math prof Richard Canary  https://plus.google.com/events/ckj6e4huqcqu5jm525vbhut45ok … #AmSciGHO pic.twitter.com/wUPfMzrlFo

   American Scientist@AmSciMag

   ·

   Tue, Feb 23 2016 20:33:10

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3. 

   American Scientist@AmSciMag

   Richard Canary works in between geometry (measuring things, distances) and topology (classifying things)  https://plus.google.com/events/ckj6e4huqcqu5jm525vbhut45ok … #AmSciGHO

   Tue, Feb 23 2016 20:34:51

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4. 

   Dianne Timblin@diannetimblin

   Richard Canary on Hollywood-style ideas of what mathematicians do:We spend more time collaborating than people think  https://twitter.com/AmSciMag/status/702229737788157952 …

   Tue, Feb 23 2016 20:35:00

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5. 

   American Scientist@AmSciMag

   Having good spatial intuition helps with topology but it also helps develop your spatial intuition as well.--Richard Canary @UMich #AmSciGHO

   Tue, Feb 23 2016 20:36:35

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6. 

   American Scientist@AmSciMag

   Math jokes on #AmSciGHO! What happens when a mathematician, engineer, and physicist wake up to a fire?  https://plus.google.com/events/ckj6e4huqcqu5jm525vbhut45ok …

   Tue, Feb 23 2016 20:38:21

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7. 

   American Scientist@AmSciMag

   The 3D space we live in has distance formulas, we can measure distance between A and B. It's known as Euclidean space.--R Canary #AmSciGHo

   Tue, Feb 23 2016 20:41:43

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8. 

   Dianne Timblin@diannetimblin

   Richard Canary: No. theory once among the most theoretical of math pursuits; now one of most useful, esp for comp sci cryptography #AmSciGHO

   Tue, Feb 23 2016 20:42:01

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9. 

   American Scientist@AmSciMag

   Hyperbolic space is different than Euclidean space. Hyperbolic space is the topic of our hangout today  https://plus.google.com/events/ckj6e4huqcqu5jm525vbhut45ok … #AmSciGHO

   Tue, Feb 23 2016 20:43:24

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10. 

    American Scientist@AmSciMag

    Euclidean space is named after the Greek mathematician Euclid  http://www.britannica.com/biography/Euclid-Greek-mathematician … #AmSciGHO

    Tue, Feb 23 2016 20:45:59

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11. 

    American Scientist@AmSciMag

    In hyperbolic space, shortest distance between 2 points is on a curved line, not a straight line like we're used to.--R. Canary #AmsciGHO

    Tue, Feb 23 2016 20:46:59

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12. 

    Dianne Timblin@diannetimblin

    R. Canary is my kind of mathematician: 15 min into the hangout & to my nerdy delight he starts sketching an example  https://twitter.com/AmSciMag/status/702229737788157952 …

    Tue, Feb 23 2016 20:51:08

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13. 

    American Scientist@AmSciMag

    More on M.C. Escher art as it relates to hyperbolic geometry  http://euler.slu.edu/escher/index.php/Hyperbolic_Geometry … #AmSciGHO

    Tue, Feb 23 2016 20:51:26

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14. 

    Dianne Timblin@diannetimblin

    R Canary: The term "hyperbolic" applies to lots of things, but they have in common exponential growth or exponential decay #AmSciGHO

    Tue, Feb 23 2016 20:55:49

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15. 

    American Scientist@AmSciMag

    Something is hyperbolic if it continues and doesn't hit a boundary. Applied to real estate, we could all live downtown--R. Canary #AmSciGHO

    Tue, Feb 23 2016 20:57:27

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16. 

    Dianne Timblin@diannetimblin

    Richard Canary: To understand mathematical space, it's important to analagize, to know what it would be like to live in that space #AmSciGHO

    Tue, Feb 23 2016 20:59:17

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17. 

    American Scientist@AmSciMag

    Richard Canary gives examples of how sports would work in hyperbolic space to help people understand hyperbolic space #AmSciGHO

    Tue, Feb 23 2016 21:00:50

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18. 

    American Scientist@AmSciMag

    In hyperbolic space, the outfield in a baseball field would have an area of over 100 digits. Think of how many outfielders! #AmSciGHo

    Tue, Feb 23 2016 21:04:45

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19. 

    Dianne Timblin@diannetimblin

    R Canary:In hyperbolic space, a high cost to traveling near apparent boundary.Closer you get to it, the longer the distance to go #AmSciGHO

    Tue, Feb 23 2016 21:04:45

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20. 

    American Scientist@AmSciMag

    While golfing in hyperbolic space, hit ball just one degree off from the hole, you would be about as far from hole than at start #AmSciGHO

    Tue, Feb 23 2016 21:07:33

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21. 

    American Scientist@AmSciMag

    People would be close to blind in hyperbolic space. You wouldn't see Titanic after it's a couple hundred feet away. --R. Canary #AmSciGHO

    Tue, Feb 23 2016 21:11:13

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22. 

    American Scientist@AmSciMag

    Baseball wouldn't be too much fun in hyperbolic space: no pitch would go over the plate. There would be a lot of walks.--R. Canary #AmSciGho

    Tue, Feb 23 2016 21:12:18

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23. See Richard Canary draw examples of sports in hyperbolic space in this video from @numberphile  https://youtu.be/u6Got0X41pY?list=PLt5AfwLFPxWIIqocD2xZGATsbe8hwpcI1 … #AmSciGho

    American Scientist@AmSciMag

    ·

    Tue, Feb 23 2016 21:17:56

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24. 

    Dianne Timblin@diannetimblin

    Richard Canary: Emergence of mathematical biology has been an exciting development in the field of math #AmSciGHO

    Tue, Feb 23 2016 21:19:12

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25. 

    American Scientist@AmSciMag

    There are contributions #math has made to sciences, that continues on. Multidisciplinary work can uncover new ideas.--R. Canary #AmSciGHO

    Tue, Feb 23 2016 21:20:17

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26. 

    Dianne Timblin@diannetimblin

    Richard Canary: A lot of folks in geometopology draw inspiration from physics. #AmSciGHO

    Tue, Feb 23 2016 21:22:44

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27. 

    American Scientist@AmSciMag

    .@AmSciMag article "In Defense of Pure Mathematics" about GH Hardy and debate over pure vs. applied #math  http://www.americanscientist.org/issues/feature/in-defense-of-pure-mathematics/1 … #AmSciGHO

    Tue, Feb 23 2016 21:23:06

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28. 

    Dianne Timblin@diannetimblin

    Richard Canary: The NSA is essentially a large organization of number theorists, encrypting and decrypting information. #AmSciGHO

    Tue, Feb 23 2016 21:23:30

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29. 

    American Scientist@AmSciMag

    If kids see themselves as not good at math, the key is to put them in a situation where they can have success with it. --R. Canary #AmSciGHO

    Tue, Feb 23 2016 21:26:37

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30. 

    American Scientist@AmSciMag

    People build up a lot of psychological blocks to success in #math if their last experience was failure.--R. Canary #AmSciGHO

    Tue, Feb 23 2016 21:27:50

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31. 

    American Scientist@AmSciMag

    At @UMich, #math students are asked to explain their calculations. "What does your result mean?"-R. Canary #AmSciGho

    Tue, Feb 23 2016 21:29:37

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32. 

    Dianne Timblin@diannetimblin

    R Canary: A lot of serendipity to scientific or mathematical discovery. 1/3 #AmSciGHO

    Tue, Feb 23 2016 21:31:58

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33. 

    Dianne Timblin@diannetimblin

    R. Canary: The serendipity of 2 researchers being in the same place at the same time, say, at a conference, can sometimes... 2/3 #AmSciGHO

    Tue, Feb 23 2016 21:33:55

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34. 

    Dianne Timblin@diannetimblin

    R. Canary: ...spark something, and an idea will emerge several years before it might have otherwise. 3/3 #AmSciGHO

    Tue, Feb 23 2016 21:34:46

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35. 

    Sarah Dunifon@SarahDunifon

    Being able to interpret the data, not just calculate it, is imperative. ESP with computers incr doing computing jobs  https://twitter.com/amscimag/status/702243941723168768 …

    Tue, Feb 23 2016 21:33:22

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36. 

    American Scientist@AmSciMag

    .@UMich #math dept is developing classes with inquiry based learning and getting students to develop #math for themselves-R Canary #AmSciGHO

    Tue, Feb 23 2016 21:33:48

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37. 

    American Scientist@AmSciMag

    Students, don't struggle on your own. "Very few people use office hours as much as they should." --R Canary, @UMich #math prof #AmSciGho

    Tue, Feb 23 2016 21:37:52

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38. 

    Dianne Timblin@diannetimblin

    Advice I wish I'd rec'd as an undergrad! If you're stuck on something, drop by during office hrs & get unstuck.  https://twitter.com/AmSciMag/status/702246020042792960 …

    Tue, Feb 23 2016 22:31:21

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39. 

    American Scientist@AmSciMag

    Thanks for watching today's Google Hangout on hyperbolic space. The recording is available  https://plus.google.com/events/ckj6e4huqcqu5jm525vbhut45ok … #AmSciGho

    Tue, Feb 23 2016 21:38:49

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40. 

    Fenella Saunders@fenellasaunders

    I had a great time discussing how topology and geometry can help us reimagine the world!  https://twitter.com/AmSciMag/status/702246665101692933 …

    @AmSciMag

    ·

    Tue, Feb 23 2016 21:48:06

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