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Chris Harrow

Magic Square -- from Wolfram MathWorld - 0 views

mathworld.wolfram.com/MagicSquare.html

Proof uniqueness

shared by Chris Harrow on 12 Nov 14 - Cached
  • Chris Harrow on 12 Nov 14
     
    Number of unique magic squares. >There is (1) 1x1 square--duh. >Interesting that there are (0) 2x2 squares.  Place any number in any corner--both adjacent corners must be the same number, preventing a square.   Can a 5th grader follow this?  >There is (1) 3x3 square. Can be reasoned out by cases. Can 5th grader follow? >There are (880) unique 4x4 squares. Very interesting that this number jumps so quickly. >Stunning:  There are (275,305,224) unique 5x5 squares.  WOW! >>We don't know how many 6x6 squares there are.  
Chris Harrow

Twitter / khanacademy: Every triangle is a right ... - 1 views

twitter.com/...1

Khanacademy right triangle Pythagorean irrational

shared by Chris Harrow on 09 Aug 14 - No Cached
  • Chris Harrow on 09 Aug 14
     
    This problem isn't remotely unique to Khan, but I'm a bit put off by the "Learn the Skill" call. That said, here are my potential additions: 1) What are the lengths of the hypotenuses? (easy) 2) How many triangles until the hypotenuse length exceeds 5 units? 3) How many triangles until the SUM of hypotenuse lengths exceeds 5 units? (never done this. How would a MS or geometry student attempt?) 4) How many triangles until the figure begins to overlap itself? (never done. How would a MS student attempt?) There must be many other GREAT problems here. Thoughts?
Chris Harrow

Devlin's Angle: Most Math Problems Do Not Have a Unique Right Answer - 1 views

devlinsangle.blogspot.be/...oblems-do-not-have-unique.html

devlin mathematics vs arithmetic computers

shared by Chris Harrow on 09 Sep 14 - No Cached
  • Knowing how to solve an equation is no longer a valuable human ability; what matters now is formulating the equation to solve that problem in the first place, and then taking the result of the machine solution to the equation and making use of it.
  • Today, we have instant access to vast amounts of information and to unlimited computing power. Both are now utilities, much like water and electricity. And that has led to a revolution in the mathematics ordinary citizens need in order to lead a fulfilling, productive life. In a world where procedural (i.e., algorithmic) mathematics is available at the push of a button, the need has shifted to what I and others have been calling mathematical thinking.
  • Unfortunately, many Americans were never taught to understand arithmetic, they were just trained to execute procedures. It's not their kids who are being short-changed. They—the parents—were!
  • Chris Harrow on 09 Sep 14
     
    Another great Devlin posting on why we need to be doing MUCH MORE thinking and pattern recognition (mathematics) and FAR LESS procedural computations (arithmetic).
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