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Unraveling Polite Numbers: Math Club Exploration

Dive into the definition of polite numbers, their characteristics, and challenges to unveil their secrets in this dynamic PowerPoint presentation. Discover the interesting world of polite numbers and their unique properties through engaging math challenges.

brenna-hardin
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Unraveling Polite Numbers: Math Club Exploration

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  1. 1+2=3 (generalized) Math Club 3/19/2012 Powerpoint Templates

  2. Definition Weshould all know that 1+2=3. A politenumberis a numberthatcanbewritten as a sum of positive consecutivenumbers. For example, 4+5+6+7 is 22, so 22 is a politenumber. Through a few challenges, wewill know everythingthereis to know about politenumbers by the end of thispowerpoint.

  3. Challenge 1 Show that 3 is a politenumber.

  4. Challenge 2 Show that 9 is a politenumber.

  5. Challenge 3 Is 4 a politenumber?

  6. Challenge 4 Find all politenumbers.

  7. Challenge 5 Show that all oddnumbers are polite.

  8. Challenge 6 Show thatanynumber divisible by 3 ispolite.

  9. Challenge 7 Provethatanynumber divisible by 7 ispolite.

  10. Challenge 8 Let besomeoddnumber. Provethat for any, infinitelymany multiples of are polite. (in otherwords, above a certain point, all multiples of are polite)

  11. Challenge 9 Challenge 8 istooweak. Let besomeoddnumber. Provethat for any, ALL multiples of are politenumbers.

  12. Challenge 10 All numberswith an odd factor are polite. Whatnumbers are left?

  13. Final Challenge (11) Show that a power of twocannotbepolite.

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