Life of Fred: Geometry Expanded Edition

 

     I became a mathematician when I took high school geometry.  That's when I changed from merely being able to do arithmetic or algebra into mathematics becoming a part of who I am.

     All of the rest of pre-college math (arithmetic, algebra, trig) is mostly mechanical.  You learn the procedures and solve the problems.  Word problems in algebra offered a little variety but after you have done a dozen word problems, they all start to look alike.

Pat can dig a ditch in 3 days.  Chris can dig it in 4 days.  How long does it take if they work together?

Pat can paint a room in 3 hours.  Chris can paint it in 4 hours.  How long does it take if they work together?

Pat can swat a dozen flies in 3 minutes.  Chris can swat a dozen flies in 4 minutes.  How long does it take if they work together?

     Geometry's central theme is finding proofs.  It is much more a creative process.  For example, we have (at least) four different ways to prove . . .

    

     Life of Fred: Geometry has much more geometry than other high school geometry books.

• Many skimp on ruler-and-compass constructions.  They might have a dozen of them.  Fred has 46 of them, including the challenging rusty compass constructions and the collapsible compass constructions.
• Some have fourth dimensional geometry.  Fred offers a Chart of the Universe that goes up to 14 dimensions.
• A chapter on symbolic logic
• Analytic geometry with slope, distance, and midpoint formulas and proofs using analytic geometry
• Non-Euclidean geometries—one of which states that in a plane, there can't exist parallel lines.

     Everyone who has had a decent course in geometry knows that Euclid's geometry, which has been studied for the last 2300 years is f-u-l-l  of  h-o-l-e-s.  

    In the last chapter of Life of Fred: Geometry we prove that every triangle is isosceles.  We prove that an angle that is greater than 90 degrees is congruent to a right angle.  We can do that because Euclid's geometry is flawed.

    An American boy (Robert L. Moore, 19) in 1899 rewrote Euclid's postulates.  He cleaned up Euclid.  No more proving untrue things.  In the last chapter of Life of Fred: Geometry we present the modern flawless geometry.  No other high school geometry book that we know of offers modern flawless geometry. 

 

     My favorite geometry theorem is:    

     I have never met a high school teacher in a government school who could prove this theorem.  (There may be some, but, so far, I haven't met one.  If you are one, please contact me—click here.  I'd be delighted to see your proof.)

    It is proved in Life of Fred: Geometry.  No other high school geometry book that we know of offers a proof.

 

   

 

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