Monday, October 7, 2013
Thursday, December 1, 2011
www.IGoogle.com Math Challenge Widget
Hi guys if you still take a look here and there at this blog! There is a cool math widget on the igoogle site if you have a google account, and use Igoogle as your homepage, you can search for "math" or "nick's math" and you will get great challenge problems to play with. I have been having fun playing with the following one...
Puzzle 159: Eight odd squares
Lagrange's Four-Square Theorem states that every positive integer can be written as the sum of at most four squares. For example, 6 = 2^2 + 1^2 + 1^2 is the sum of three squares. Given this theorem, prove that any positive multiple of 8 can be written as the sum of eight odd squares.
...I can prove that every odd square is a multiple of 8 +1, and show a few initial cases of odd squares adding up to consecutive multiples of 8, but still working on how to prove that every multiple of 8 can be written as the sum of eight odd squares.
Feel free to give it a try and show me what you have gotten!
Puzzle 159: Eight odd squares
Lagrange's Four-Square Theorem states that every positive integer can be written as the sum of at most four squares. For example, 6 = 2^2 + 1^2 + 1^2 is the sum of three squares. Given this theorem, prove that any positive multiple of 8 can be written as the sum of eight odd squares.
...I can prove that every odd square is a multiple of 8 +1, and show a few initial cases of odd squares adding up to consecutive multiples of 8, but still working on how to prove that every multiple of 8 can be written as the sum of eight odd squares.
Feel free to give it a try and show me what you have gotten!
Tuesday, November 22, 2011
Goodbye Grade 10 and 11 IRHS Mathies!
For those who like to take a look at this blog, I will try to add challenges here and there for you to try! Feel free to post comments or suggestions of things you would like to see on here if you really enjoy it! As you get into 11th and 12th grade math and beyond, please do use me as a resource for you when you need some guidance!
I will miss all you guys at IRHS and I wish you all success and happiness in your future endeavors! Sad to leave, but happy to have been a stepping stone on your learning journeys (corny I know, but true!)
Thank you
I will miss all you guys at IRHS and I wish you all success and happiness in your future endeavors! Sad to leave, but happy to have been a stepping stone on your learning journeys (corny I know, but true!)
Thank you
Monday, November 21, 2011
Tuesday, November 15, 2011
Wednesday, November 9, 2011
New Challenge!! Triangle Area Ratios
What is the Relationship between Triangles?
In triangle ABC, segment AG from vertex A meets opposite side BC at a point G, with the length of CG 1/3 the length of BC. That is, point G is located 1/3 of the way along segment BC from C. Similarly, points E and F are located at 1/3 marks along the other two sides of triangle ABC. The intersections of these segments are the vertices of another triangle, IJH, in the interior of triangle ABC.
What is the relationship between the areas of triangles ABC and IJH?
Tuesday, October 25, 2011
Factory Balls: Best logic game ever
Note to self: Don't start this unless you have time to spare! It's as addicting as Snood once was
http://hoodamath.com/games/factoryballs2.php
http://hoodamath.com/games/factoryballs2.php
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