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great topics to investigate

Discussion in 'Mathematics' started by mollycoddles, Nov 5, 2019.

  1. mollycoddles

    mollycoddles New commenter

    Hi all,
    can anyone recommend a couple of mathematical topics that would be useful as material for my top mathematicians to investigate as a more extended project? I'm thinking something like mondrian squares.... or an interesting version of the old GCSE coursework tasks.
    Can be applied or pure maths.
    Please bombard me with a few idea's to investigate.
     
  2. gainly

    gainly Lead commenter

    Which right angle triangles with sides of integer value have the perimeter numerically equal to the area? Can you prove these are the only ones?

    Investigate how the hours of daylight (sunrise to sunset) vary throughout the year for cities at different latitude. Find equations for individual cities. Is it possible to find a general equation?
     
    mollycoddles likes this.
  3. mollycoddles

    mollycoddles New commenter

    Thank you! Great starting point. I particularly like the one about day
    GitHub hours one.
     
  4. gainly

    gainly Lead commenter

    Glad you like them.

    The right angle triangle proof is quite difficult although it only uses GCSE maths.

    The daylight hours data for individual cities fit quite well to a sine curve, obviously with different constants depending on latitude. I'm not actually sure if there is a simple equation relating the constants to latitude.
     
  5. mollycoddles

    mollycoddles New commenter

    Apologies about my typo. Missed it late last night. Is there a website you’d recommend that has a few more similar ideas? Could use approx 5 or 6 more and struggling to come up with them.

     
  6. gainly

    gainly Lead commenter

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