SPS SP2171 Heavenly Mathematics Tutorial

  1. How do we know that the Earth is round?
  2. Suppose you work as a real estate agent in Norway and you're looking at an apartment with a balcony. Which direction do you hope the balcony is facing? What if you work in Australia? Do Singaporeans prefer “morning Sun” or “afternoon Sun”?
  3. How does the distance between the northernmost and the southernmost rising position of the Sun depend on the latitude? What is the distance in Singapore? What is the distance just south of the Arctic Circle?
  4. Pick a window in the SPS Room. Use a compass and the hand techniques for estimating angles in the sky to estimate what parts of the daily paths of the Sun on the solstices and equinoxes can be seen from the window. Discuss which months and during what time of the day you will see the Sun from the window. I'm not expecting exact values, just reasonable estimates that shows that you have learned the key concepts about the motion of the Sun.
  5. As I explained, your Chinese and Western birthdays will usually coincide on your 19th birthday. However, when I give public lectures at schools, and try it out on the students, I find that some years it works very well, and some years it doesn't work so well. How can you explain that?
  6. Between 1900 and 2100, Chinese New Year and Valentine Day coincides for 1915, 1934, 1953, 2010, 2048, 2067, 2086. If somebody asks you how often the two dates are likely to coincide in a century, what would your first estimate be? What do you notice about these years?

Helmer Aslaksen
Department of Mathematics
National University of Singapore

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