Good evening everyone!
    It's you're favorite french speaking Filipino
giving you the low down on today's class.
(I real...
Thank you for selecting English...




                        Philosopher, physicist, mathematician.  
                  ...
         Pascal         1
                 Pascal's Triangle  simplifies grunt work 
                     for solving bino...
(a + b)0 = 1
                   (a + b)1 = 1a  + 1b
              (a + b)2 = 1a2 + 2ab  + 1b2
          (a + b)3 = 1a3 + 3...
All right! Let's look for 
some creepy patterns!
Creepy 
Pattern #1
                               4 +6




              ...
Creepy 
Pattern #2


    110 = 1                       1
                                11
   111 = 1 1                  ...
Creepy 
Pattern #3                   Okay NOW this was
                        starting to look like a David
             ...
Creepy                 (a + b)0 = 1
 Pattern #4         (a + b)1 = 1a  + 1b
               (a + b)2 = 1a2 + 2ab  + 1b2
   ...
Creepy 
Pattern #5


         1
        11
       121
      1331
     14641
   1 5 10 10 5 1
 1 6 15 20 15 6 1
1 7 21 35 3...
No further explanation needed...



                                   10
Phew!
   That took longer than it needed it to be.  Too 
many magic tricks in this unit.  Everything is just 
beginning to...
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  1. 1. Good evening everyone! It's you're favorite french speaking Filipino giving you the low down on today's class. (I really can't speak french) To begin, please select your preferred language: French English X 1
  2. 2. Thank you for selecting English... Philosopher, physicist, mathematician.   Discoverer of Probability.   The impossible search for Truth. His name was Blaise Pascal. Blaise Pascal has led to many expositions including the famous Pascal Triangle! This triangle is an inventory of Binomial Coefficients, and the patterns, and relationships it contains. 2
  3. 3.          Pascal         1 Pascal's Triangle  simplifies grunt work  for solving binomial equations that Triangle    1 1 can take a huge amount of time 121 that everyone doesn't have. 1331 (Thank you Pascal)   14641 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 Let's do some binomial equations to show you how this triangle relates to these equations... 3
  4. 4. (a + b)0 = 1 (a + b)1 = 1a  + 1b (a + b)2 = 1a2 + 2ab  + 1b2 (a + b)3 = 1a3 + 3a2b + 3ab2  + 1b3 (a + b)4 = 1a4 + 4a3b + 6a2b2 + 4ab3 +1b4 (a + b)5 = 1a5 + 5a4b + 10a3b2 + 10a2b3 + 5ab4 + 1b5 WOH! Check hizzout the  1 coefficients of the  11 equations above, and the  121 1331 numbers in the triangle:     14641 Strikingly similar! 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 4
  5. 5. All right! Let's look for  some creepy patterns! Creepy  Pattern #1 4 +6 = 1 11 121 10 1331 14641 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 Take any number, any number at all! (From the table) Then take the 2 numbers above it, and add it! oOoOo I'm not even at the good part yet. 5
  6. 6. Creepy  Pattern #2 110 = 1 1 11 111 = 1 1 121 1331 112 = 1 2 1 14641 113 = 1 3 3 1 1 5 10 10 5 1 1 6 15 20 15 6 1 114 = 1 4 6 4 1 1 7 21 35 35 21 7 1 This is when I started to think witchcraft had something to do with it... hmm 6
  7. 7. Creepy  Pattern #3 Okay NOW this was starting to look like a David Blane trick. Make a diagonal line going downwards starting 1 anywhere for as long as you 11 want it to be. Then bend 121 the diagonal line the other 1331 direction for two rows as 14641 shown in the diagram to the 1 5 10 10 5 1 left. The LAST number is the 1 6 15 20 15 6 1 sum of all the number's 1 7 21 35 35 21 7 1 selected before it!! AHH! It's a hockey stick!! 7
  8. 8. Creepy  (a + b)0 = 1 Pattern #4 (a + b)1 = 1a  + 1b (a + b)2 = 1a2 + 2ab  + 1b2 (a + b)3 = 1a3 + 3a2b + 3ab2  + 1b3 (a + b)4 = 1a4 + 4a3b + 6a2b2 + 4ab3 +1b4 (a + b)5 = 1a5 + 5a4b + 10a3b2 + 10a2b3 + 5ab4 + 1b5 In each increasing From the last term, term, the variable Look at the variable 'a,' the variable 'b' is 'a' is decreasing by and its exponents. The 1. increasing as you exponent of 'a' of the move up the first term is the same terms, and is also number as the number the same number you're quot;poweringquot; in you're quot;poweringquot; (a+b). in (a+b) 8
  9. 9. Creepy  Pattern #5 1 11 121 1331 14641 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 It just doesn't stop... 9
  10. 10. No further explanation needed... 10
  11. 11. Phew! That took longer than it needed it to be.  Too  many magic tricks in this unit.  Everything is just  beginning to unfold though, can't wait to see what  Monsieur Kurapatwa has to reveal tomorrow. Wohoo! scribe picking time! I ch­ch­choooose: Haiyan! !nayiaH  11

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