Day 6 in Mat115H

Today:

• Announcements
  • Homework for the "Beaver's Tail" poems is returned
    • I'm focused partly (maybe even mostly) on your writing in this sort of exercise.
    • Remember to type these sort of submissions up (unless I tell you otherwise, assume that it should be typed).
    • Would anyone like to pay a poem a complement?
  • Your mobius band homework is due.
  • Your assignment for next time:
    Continue working on bases, and finish Fit the Second; Begin Fit the Third.

• A note about symmetry and the Mobius band:

  • My apologies: Fortunatus's Purse and the Klein Bottle are different!
  • I discovered this using our diagram and another type of symmetry.
  • As our author notes, Fortunatus's Purse is the "real projective plane", which is topologically distinct from the Klein bottle (although both are non-orientable).

• More about Charles Dodgson:
  • Family
    1. Father gave up Studentship to marry his first cousin.
    2. Eldest of four sons; seven sisters
    3. Poor until they moved to Croft
    4. Family life improved upon moving to Croft
    5. Spent his 1st eleven years in "deep countryside"
    6. Created a family magazine and entertained the family
    7. Raised in a strict Christian family
    8. while he was at school, he often wrote letters to his family, especially his sisters (throughout chapter)
    9. studied at Christ Church where his father studied
    10. his father wrote letters to the headmasters to make sure his son did not get awards or good grades due to favoritism
    11. his father taught him Latin, math, english lit, and theology
    12. Healthy - they all survived to adulthood which was rare in the old days
    13. Leader of the pack - He quickly became the leader of the siblings. He liked to enterta in them and whatnot
    14. Spiritual - They often read the bible and attended church services.
    15. Smart - If his parents were the ones teaching him, they must have been pretty smart themselves.
    16. Close- They stuck together through being poor, home schooling, moving, etc.
    17. All siblings survived to adulthood. (pg 23)
    18. Father well connected, as the headmasters of Richmond and Rugby schools wrote to him about Charles Jr. (pg 25, 29)
    19. Close to sister Elizabeth, as seen in his letters home. (pg 33)
    20. All but one of his siblings (Edwin) born at Daresbury. (pg 23)
    21. Father very involved in community; started a Sunday school, lectured. (pg 24)
    22. His father became the Rector of the parish church of St. Peters and the entire family moved to Croft.
    23. The family struggled financially until Charles Dodgson Sr. received a raise with his new position as Rector.

  • Religion
    1. attended Christ Church as a student
    2. his father was a reverend at St.Peter's
    3. his spirituality and religious conviction "governed his future life" (p.24)
    4. the headmaster of Rugby, where Lewis went to school, later became the Archbishop of Canterbury (p.33)
    5. at the Christ Church, terms were determined by the Liturgical seasons
    6. His religious values must have stayed with him because when the book talks about the bullies, he never fights them back. He just takes it
    7. Father an ordained priest. (pg 23)
    8. Religious views remained with him his entire life. (pg 24)
    9. Sent to school to prepare him for the church. (pg 27)
    10. Religion an important aspect of Richmond and Rugby's curriculum. (pg 27, 32)
    11. Able to move to Croft through father's connection to clergy. (pg 25)

  • Education
    1. Educated at home by his father
    2. At 12 he went to Richmond
    3. attended Rugby school in 1846 (p. 31)
    4. went to Oxford University (p. 39)
    5. top of the class in his mathematics class at Oxford (p. 51)
    6. attended Christ Church as a student (p.53)
    7. lost out on a senior scholarship (p.55)
    8. Awarded many scholastic awards
    9. Well respected by his teachers because he was so intelligent
    10. Loner- He never really made many friends while attending school
    11. Smart- He was always intelligent, even from an early age and was awarded many things throughout his life
    12. Taught maths, Latin, theology, and English literature by his father at Daresbury. (pg 24)
    13. At Richmond focus was on religion and literature, maths was an extra. (pg 28-29)
    14. Could write fluent Latin by Richmond. (pg 31)
    15. Received numerous awards for academics at Rugby. (pg 32)
    16. Excelled in other areas than math. (pg 34)
    17. Could compose latin verse by age 12.
    18. While at Rugby School, he received awards in mathmatics, history, divinity, Latin composition and English.
    19. Preferred private school over public school.
    20. Left a lasting impression on almost all of his teachers and headmasters.
    21. Attended Oxford University

  • Character
    1. Creative
    2. Leader
    3. Family-oriented
    4. Did well in school
    5. Strong Christian Character
    6. Desire to Learn
    7. Persistent
    8. acknowledged his intellect (p.53)
    9. could be cocky (p.53)
    10. wrote stories and poems for the local newspapers (p.48)
    11. became close friends with his professor, Professor Whit (p.48)
    12. spent lots of time preparing to teach students (p.55)
    13. Well Rounded- He not only was a mathematician, but he composed latin verse
    14. Mature- He had knowledge that was far beyond his years
    15. Weak- He was bullied at Rugby school and was deaf in one ear because of it
    16. Determined- He knew what he wanted (to learn) and he was willing to do anything to get it
    17. Curious- Even though his father told him he wouldn't be able to understand a certain math problem, Lewis still wanted to learn about how it was done.
    18. Loved animals. (pg 23)
    19. Built a maze that "rivalled" Hampton Court's. (pg 27)
    20. Lifelong interest in astronomy. (pg 27)
    21. Didn't take well to bullying. (pg 31)
    22. Liked to educate and challenge siblings. (pg 34)
    23. While living in Daresbury, he made friends with odd and unlikely animals.
    24. He had a vivid imagination from a very early age
    25. Suffered from bullying while at Rugby School
    26. Took sick frequently
    27. Looked up to his father and wished to be like him

  • Geography
    1. At Daresbury childhood isolated and uneventful. (pg 21)
    2. Idyllic childhood at Croft. (pg 25)
    3. Ill health took in at Rugby, which had lasting effects. (pg 31)
    4. Return to Croft, Dodgson develops two specific difficulties. (pg 34)
    5. Richmond first non-domestic education environment. (pg 27)

  • Questions:
    • this isn't a fact, but I was wondering if any of Lewis Carroll's brothers or sisters got to attend school because it did not mention it in the book.

• We'll take a look at a few of the problems in the Arithmetic text (p. 30).

• What do you think of (the evident fact) that children at such a young age were expected to be able to reason so well? Do you think that society would be wise to return to such expectations for our kids?

  A joke (sort of!)

• About time:
  • International Date Line
  • A stopped versus a slow clock....

• About bases!
  • Here's the handout for background
  • The Great Fraudini
  • Tom Lehrer sings about bases (here are the lyrics - local copy). Here's a math club member lip-syncing it!
  • How was Carroll using bases to do the math in chapter two of Alice in Wonderland? On about the third page of chapter two, Alice starts speaking out some bizarre equations:

    "Let me see: four times five is twelve, and four times six is thirteen, and four times seven is -- oh dear! I shall never get to twenty at that rate!"