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Thread: Determinant Demonstraition

  1. #1
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    Default Determinant Demonstration

    Ok, math lesson time! The determinant of a 2 X 2 matrix (ad - bc) gives the area of the parallelogram spanned by the two 2D vectors (a,b) and (c,d) which are the rows of the matrix. This is proved with algebra and the students have no idea why it is geometrically true. For years, I have told my students there must be a way draw triangles and see that it is true. I had never done it but I new it must be possible because it is true! Well I finally put some time into it and discovered a most pleasing geometric proof. I have never, in my 25 years of teaching seen this proof before. I is so simple, I cannot understand why it is not all over the internet.

    So here is my demo carved out of walnut with arbutus triangles. Can you see why the area of the parallelogram is equal to the determinant (difference of the area of the large square and the small square) ?
    Attached Thumbnails Attached Thumbnails determinant 1.jpg   determinant 2.jpg  
    Last edited by bergerud; 06-29-2013 at 11:59 AM.

  2. #2
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    Default

    Beautiful work, but I would understand the explanation better if it weren't written in Greek. That is why I stopped at an associates degree.
    CarveWright StartU team member
    Web Site WWW.clintscustomcarving.com

  3. #3
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    Clever indeed!
    Steve

  4. #4
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    I understood that completely! They were words typed on a page. LOLI have an old friend from school who is a math professor, want me to show it to him?
    "Carved with Love"

    Happiness comes from within.
    But joy comes from helping others.

    Measure twice... and then sneak up on it!

  5. #5
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    Quote Originally Posted by badbert View Post
    I understood that completely! They were words typed on a page. LOLI have an old friend from school who is a math professor, want me to show it to him?
    Sure, ask him is he has ever see it before. It is so simple, I cannot believe it is not in textbooks.

  6. #6
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    I can see what you mean but I didn't finish high school I got my ged years later and it was from what I learned over the years as being a welder I could not comprehend ..y equaled to z and I don't know y...lol

  7. #7
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    Eureka...Although that was volume not area, but still worthy of one.

    dave

  8. #8
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    Bergerud that's very good, now do you think you could show us a Beal conjecture with the CW?
    thanks so much!
    karl

  9. #9
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    Quote Originally Posted by gashawk View Post
    Bergerud that's very good, now do you think you could show us a Beal conjecture with the CW?
    I do not think so. That is a pure number theory thing with no connection to geometry (since the exponents > 2) that I can see.

  10. #10
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    that thing hurts my head

    But looks great. Real nice job on the fit.

    Lawrence

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