• Vocabulary for "Looking for Pythagoras"

    Square - A two-dimensional figure with 4, congruent sides and 4 right angles.  A type of rectangle.

     

    Perfect square numbers - numbers (of tiles) that can be form a square.  The square root of a perfect square number is a whole number (or integer if considering the negative square root). A whole number squared is a perfect square number. The first ten perfect square numbers are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

     

     Area - the number of squares (square units) within the perimeter of a figure.  The surface area of a 3 dimensional figure is the number of squares on its surface. Area is always measured in square units.  A square cm is 1 cm by 1 cm, a square inch is 1 inch by 1 inch, etc.

     

    Square a number

     

    square root

     

    Click the link below to see a short video on estimating square roots.  It also includes how to simplify square roots.

    https://www.educreations.com/lesson/view/simplify-square-roots/18714052/?ref=appemail

     

    Click the link below to get view a video showing a strategy to convert repeating decimals to fractions

    http://www.educreations.com/lesson/view/repeating-decimals/18545616/?ref=appemail

     

    Click the link below to see a video with a different strategy to convert repeating decimals to fractions

    http://www.educreations.com/lesson/view/repeating-decimals-2/25803892/?ref=appemail

     

    Natural numbers - counting numbers (positive numbers with no fractions or decimals).   1,2,3,4,...

    Whole numbers - the natural numbers and 0.   0,1,2,3,....

    Integers - the whole numbers and their opposites. ...,-3,-2,-1,0,1,2,3,...

    Rational numbers - any number that can be written as a fraction (integer/integer).  This includes all integers, fractions, decimals that end, and decimals that repeat, but never end.

    Irrational numbers - numbers that cannot be written as fractions - decimals that go on forever with no repeating patterns.  Includes pi, and many square roots.

    Real numbers - the set of all rational and irrational numbers

     

    Make a Square

     

    The Pythgaorean Theorem

     

    Converse of Pythag Thm

    Right?  

     

    PROOFS OF THE PYTHAGOREAN THEOREM (these prove that the Pythagorean Theorem works for any right triangle. This is not the same as the main idea behind the Pythagorean Theorem or how it works. The main idea is that the sum of the areas of the squares placed on the legs of right triangle is equal to the area of the square placed on the hypotenuse).

    **note** To meet the standard, you need to understand and be able to explain one proof of the Pythagorean Theorem.  To exceed the standard, you need to understand and be able to explain more than one proof.  You do not need to understand them all.  Below, you will find links for some of the different proofs. There are hundreds more out there if you wish to further explore.

     

    Pythagoras' geometrical proof (the one that we examined in class based on the puzzles we cut out):

    https://www.educreations.com/lesson/view/pythagoras-proof/37875702/?s=8kTxy0&ref=appemail

     

    An algebraic look at Pythagoras' proof:

    https://www.educreations.com/lesson/view/algebraic-proof/37875877/?s=EhOPI9&ref=appemail

     

    Bhaskara's First Proof (similar to the algebraic version of Pythagoras' proof):

    https://www.educreations.com/lesson/view/bhaskara-s-first-proof/37876043/?ref=appemail

     

    Bhaskara's Second Proof (this requires an understanding of similar triangles):

    https://www.educreations.com/lesson/view/bhaskara-s-second-proof/37876337/?s=Cp0mTj&ref=appemail

     

    Garfield's Proof (this requires an understanding of how to find the area of a trapezoid):

    https://www.educreations.com/lesson/view/garfield-s-proof/37876553/?s=nhnyvf&ref=appemail