Thursday, July 08, 2010

Hi Johnny! Have your dad show you why the sum of the squares of the sides of a right triangle equals the square of the hypotenuse ...

He can use the little diagrams (that I borrowed from Mr. GOOGLE) below if he wishes. (Click on it to make it a tad more readable!)





The diagram below is clearer to read, but you would have to compute the areas and write the equations out. Then again, what the heck--here's the "work."

Area of each triangle is ab/2. The large square is (a+b)^2

Thus (a + b)^2 – 4(ab/2)= c^2 or A^2 + b^2= c^2




Ask your geometry teacher to prove the Pythagorean Theorem and let's see how quickly he/she comes up with a solution ... there are dozens on the Internet.

Love

Grandpa

7 Comments:

At 2:39 PM, Anonymous Anonymous said...

Way to go Joe, because every boy needs a Grand-Father like you willing to go the long hall for their grand-kids. From someone that thinks your a great grand-father and father and friend and a
all a long great person.

 
At 8:17 PM, Blogger Dr. Joe said...

I an NOT a "great grandfather" but my kid sister is a great grandmother ... TWICE!!

 
At 4:33 AM, Anonymous Anonymous said...

Dr. Joe,

Mr. P let me know of your wonderful website - a motley assortment of news topics intermingled with mathematical and physical short pieces.

The proof of Pythagorean's thereom you shared was very simple! How about sharing the proofs of the Circumference of a circle = pi*diameter or the Area of a cirlce = pi*radius^2?

Thank you,

Mrs. S

 
At 2:52 PM, Blogger mediawingnuts said...

What's this? A challenge? Pi was originally DEFINED to be the circumference of a circle divided by its diameter. Showing that that is equal to the familiar infinite series is the challenge--although here again, we need only invent trigonometry to take that baby step ... or use calculus and introduce Euler's "e" function.

JR

 
At 3:32 PM, Blogger Dr. Joe said...

For my grandson, let's simplify the problem:

Suppose pi = 3 (exactly).

Then ... the following steps resolve the issue without reference even to laws passed (almost) in both Indiana and Tennessee plus various other references including the Holy Bible:

Step 1: pi = 3
Step 2: (multiply both sides by 0)
Step 3: 0 = 0
Which is True!

Therefore pi is exactly 3. QED.

 
At 7:01 PM, Anonymous Anonymous said...

Dr. Joe,

I will take your word that pi was defined as the Cirumference of a Circle divided by it's Diameter.

Can it be proven that the area of a circle=pi*r^2?

I have many more questions I would like to ask the fine Dr., but let's start here.

Thank you,

Mrs. S.

 
At 11:44 AM, Blogger Dr. Joe said...

Mrs. S.:

See new posting above!

Dr. Joe

 

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