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[Music]
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[Music]
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thank you
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[Music]
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[Music]
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strange
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[Music]
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[Music]
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okay creature
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foreign
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[Music]
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hello
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hello Donald
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mathematic land
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Wisconsin land
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on
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it's the land of Great Adventure
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now who are you
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I'm a spirit the true Spirit of
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Adventure that's for me what's next
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a journey through the Wonderland of
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mathematics where that that's for all
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times hey kids now hold on Donald you
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like music don't You
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well without Eggheads there would be no
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music
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come on
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let's go to ancient Greece
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the time of Pythagoras the master
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Egghead of them all well fatherless the
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father of mathematics and music
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ah you'll find mathematics in the
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darndest places
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watch
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first we'll need a string
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stretch it good and tight plunk it
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now divide in half plonk again
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[Music]
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you see it's the same tone one octave
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higher now divide the next section
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and the next
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Pythagoras discovered the octave had a
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ratio of two to one
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with simple fractions he got this
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[Music]
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this harmony in numbers developed the
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musical scale of today
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[Music]
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bye daddy you do so much magic gorgeous
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glitches you can imagine how excited
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Pythagoras was when he shared his
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findings with his Pals a fraternity of
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Eggheads known as the pythagoreans
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they used to meet in secret to discuss
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their mathematical discoveries
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only members were allowed to attend they
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had a secret emblem the pentagram
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[Music]
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let's see what the topic is for today
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[Music]
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what's going on
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it's a jam session
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[Music]
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was a Beat
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[Music]
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okay
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[Music]
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so from these Eggheads the pythagoreans
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with their mathematical formula came the
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basis of our music of today
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[Music]
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[Music]
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thank you
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[Music]
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laughs
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[Music]
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foreign
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[Music]
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it was our old friend Pythagoras who
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discovered that the pentagram was full
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of mathematics
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foreign
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the two shorter lines combined exactly
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equal the third and this line shows the
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magic proportions of the famous golden
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section
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the second and third lines exactly equal
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the fourth once again we have the golden
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section
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this is only the beginning
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hidden within the pentagram is a secret
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for creating a golden rectangle which
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the Greeks admired for its beautiful
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proportions and Magic qualities
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the star contains the golden rectangle
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many times over
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[Music]
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it's a most remarkable shape it can
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mathematically reproduce itself
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indefinitely
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all these rectangles have exactly the
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same proportions
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[Music]
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this figure also contains a magic spiral
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that repeats the proportions of the
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golden section into Infinity
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to the Greeks the golden rectangle
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represented a mathematical law of beauty
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we find it in their classical
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architecture
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the Parthenon perhaps one of the most
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famous of early Greek buildings contains
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many golden rectangles
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[Music]
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these same golden proportions are also
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found in their sculpture
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foreign
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foreign
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[Music]
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that followed the golden rectangle
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dominated the idea of beauty and
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architecture throughout the Western
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world
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the Cathedral of Notre Dame is an
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outstanding example
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Renaissance painters knew this secret
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well
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[Music]
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today the golden rectangle is very much
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a part of our modern world
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[Music]
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modern painters have rediscovered the
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magic of these proportions
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indeed this ideal proportion is to be
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found in life itself
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[Music]
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not quite
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now I'm afraid
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[Music]
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well we can't all be mathematically
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perfect
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[Music]
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[Applause]
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I knew I could do it now that you're all
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pent up in a pentagon let's see how
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nature uses the same mathematical form
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petunia
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[Music]
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the star jasmine
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[Music]
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the starfish
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the wax flowered
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there are literally thousands of members
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in good standing in Nature's Pythagorean
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Society of the star
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God
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[Music]
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all Nature's Works have a mathematical
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logic and her patterns are Limitless
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[Music]
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the magic proportions of the golden
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section are often found in the spirals
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of Nature's designs
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[Music]
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[Applause]
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the profusion of mathematical forms
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brings to mind the words of Pythagoras
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everything is arranged according to
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number and mathematical shape
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yes there is mathematics in music in art
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in just about everything
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and as the Greeks had guessed the rules
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are always the same
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[Music]
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well Donald did you enjoy your
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geometrical Journey
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that's right Donald and you can find
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mathematics in games too
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let's begin with a game that's played on
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squares
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no chess chess a mathematical contest
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between two minds it's a game that has
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been enjoyed for Centuries by Kings and
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Communists in fact Lewis Carroll a
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famous mathematician with a literary
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mind used chess as a setting for his
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classic tale Through the Looking Glass
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Alice found herself face to face with an
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unto-friendly group of chess pieces good
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Heavens what's this on my soul it
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appears to be a lost Pawn
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says he's Donald Duck
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Preposterous or it could be an ALICE
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[Music]
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Alice no no no no it's a lost Pawn
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lost Pawn
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stop that pawn
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[Music]
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foreign
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[Music]
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now you can look at this game from a
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safer perspective
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[Music]
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chess is a game of calculated strategy
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and since the board is geometrical the
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moves are mathematical
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[Music]
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Checkmate and the game is over
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here watch dogs practically all games
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are played on geometrical areas
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the baseball field is a diamond I
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[Music]
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can't keep score
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football is played on a rectangle
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divided by yard lines
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[Music]
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basketball is a game of circles spheres
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and rectangles
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even Hopscotch has its multiple squares
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[Music]
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what's next
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no a mathematical game played on a field
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of two perfect squares
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using three perfect spheres and a lot of
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diamonds in other words Billiards
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[Music]
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for me you know the game don't you
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Donald
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gosh
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yes
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[Music]
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now let's see how an expert at three
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cushion Billiards uses his head
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it only has to hit both the other balls
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but it must contact at least three
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cushions before it hits the final ball
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[Music]
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one two three
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[Music]
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thank you
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one two three
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[Music]
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it takes an expert to make several shots
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in succession
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one two
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three four
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[Music]
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five six
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[Music]
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getting shot
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luck no it's skill
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for this game you have to know all the
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angles
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[Music]
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[Music]
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first there's technique he's striking
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the cube ball low so it'll spin
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backwards
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hitting the ball on the right side will
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make it hug the rail
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these trick shots take a lot of practice
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one two
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[Music]
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three
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oh this game takes precise calculation
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he figures out each shot in his head
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he could play it like this but it calls
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for quite a bit of luck there is a
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better choice for this he uses the
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diamond markings on the rail as a
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mathematical guide first he figures the
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natural angle for hitting the object
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balls and then he finds that his cue
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ball must bounce off the number three
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Diamond next he gets ready for the shot
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and he needs a number for his Q position
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the SE calls for a different set of
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numbers
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[Music]
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not when you get the hang of it you see
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the Q position is four
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now a simple subtraction three from four
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is one
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so if he shoots for the first diamond he
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should make it it's called playing the
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diamond system
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natural angle two
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position one and a half two two and a
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half three three and a half two from
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three and a half is one and a half so
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shoot halfway between the first and
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second diamonds
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[Music]
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Instagram
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foreign
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there's no guesswork to mathematics it's
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quite simple natural angle for the hit
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two cue position three and a half how
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much is three and a half minus two
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[Music]
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wow
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[Music]
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you're making it tough for yourself
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Donald
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[Applause]
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[Music]
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wonderful Donald and now you're ready
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for the most exciting game of all
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and the playing field for this game is
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in the mind
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oh look at the condition of your mind
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Antiquated ideas bundling false Concepts
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superstitions
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confusion to think straight we'll have
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to clean house
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[Music]
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all right
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there that's more like it a nice clean
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sweep
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this game is played with circles and
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triangles think of a perfect circle
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[Music]
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perfect
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Circle
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perfect
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Circle
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please
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perfect
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ah put a triangle inside and turn it now
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spin the circle and what have you got
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foreign
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[Music]
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the shape of things is first discovered
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in the mind
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slice off the top and we have a
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reminder
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that's right
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a lens is a section of a sphere all
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Optical instruments are created through
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mathematics
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[Music]
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you see there's a lot more to
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mathematics than just numbers and
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equations
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let's get back to our Circle and
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triangle
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[Music]
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roll it and we have a uh
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[Music]
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the circle has been the basis for many
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of man's important inventions
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[Music]
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the mind can create the most amazing
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things
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if we spin the triangle we have a
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slice the cone the cone is full of
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useful mathematical shapes
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[Music]
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slice it again slice it several times
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[Music]
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the orbits of all planets and satellites
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can be found in the cone
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no matter how you slice it it's always
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mathematics
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a slice like this gives us the reflector
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of a Searchlight
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a slice like this the mirror of a giant
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telescope
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a line on a cone and we have a drill
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and the spring
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now you're ticking
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[Music]
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number please
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[Music]
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the mind is the birthplace for all of
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man's scientific achievements
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okay
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[Music]
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the Mind Knows No Limits when used
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properly
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think of a pentagram Donald
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now put another inside a third
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and a fourth no pencil is sharp enough
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to draw as fine as you can think
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and no paper large enough to hold your
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imagination
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in fact it is only in the mind that we
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can conceive Infinity
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mathematical thinking has opened the
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doors to the exciting Adventures of
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science
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[Music]
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each Discovery leads to many others an
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endless chain
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of course they are locked these are the
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doors of the future and the key is
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bottles right
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mathematics the boundless Treasures of
00:27:08
science are locked behind those doors
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in time they will be opened by the
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curious and inquiring minds of future
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Generations
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in the words of Galileo
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mathematics is the alphabet with which
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God has written the universe
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[Music]
