"Donald in Mathmagic Land" (4K AI Upscale)

00:27:43
https://www.youtube.com/watch?v=hl6JDv4ZG7U

الملخص

TLDRThe video takes viewers on a journey through the world of mathematics, music, and nature, starting with Pythagoras, who discovered the relationship between mathematics and musical harmony. It explains how the golden ratio and geometric principles, such as the pentagram and golden rectangles, represent beauty in art and architecture. The video also illustrates how mathematics is utilized in various games, emphasizing calculated strategy in chess and billiards. Nature's patterns, governed by mathematical logic, further reinforce the idea that mathematics is integral to understanding and appreciating the universe, as expressed in Galileo's quote about the language of mathematics.

الوجبات الجاهزة

  • 🎶 Mathematics and music are deeply intertwined.
  • 📏 The golden ratio represents beauty in art and nature.
  • 🎲 Games like chess and billiards rely on mathematical strategies.
  • 🏛️ The golden rectangle can be found in classical architecture.
  • 🌿 Nature follows mathematical patterns remarkably.
  • 🧠 The mind is crucial for understanding complex mathematical concepts.
  • 🔢 Pythagoras discovered musical harmony through numbers.
  • 🔑 Mathematics unlocks the doors to scientific discoveries.
  • 🌌 Galileo claimed math is the language of the universe.
  • 🔄 Mathematical principles repeat infinitely in nature.

الجدول الزمني

  • 00:00:00 - 00:05:00

    The introduction features a spirit of adventure, leading Donald Duck on a journey through the realm of mathematics and its connection to music. They visit ancient Greece, where Pythagoras explores the relationship between mathematics and musical tones through string division, discovering that an octave has a 2:1 ratio, which developed today’s musical scale.

  • 00:05:00 - 00:10:00

    The Pythagoreans’ secret gatherings are highlighted, where they discussed mathematical discoveries and secrets intertwined with music. The pentagram symbolizes their knowledge, and its hidden mathematical properties are revealed, containing relationships that conform to the golden section—a proportion admired by Greek mathematicians for its beauty.

  • 00:10:00 - 00:15:00

    The concept of the golden rectangle and its representation in nature and architecture is explored, showing how this ratio permeates Greek classical architecture like the Parthenon. It illustrates that many forms of beauty in art and nature are derived from fundamental mathematical principles, emphasizing the connection between mathematics and aesthetics throughout history.

  • 00:15:00 - 00:20:00

    Games, particularly chess, are introduced as a mathematical strategy, showcasing the geometric nature of game boards. Various sports are discussed, revealing the underlying mathematical principles, such as angles and measurements in billiards, demonstrating how mathematics permeates everyday activities and strategic thinking.

  • 00:20:00 - 00:27:43

    The narrative comes full circle as it emphasizes the limitless potential of the mind in creating and innovating through mathematics. Concepts like lenses from cones and other inventions highlight that mathematics isn't just numbers—it's foundational to scientific exploration and advancements, underscoring Galileo's assertion that mathematics is the universe's language.

اعرض المزيد

الخريطة الذهنية

فيديو أسئلة وأجوبة

  • Who is Pythagoras?

    Pythagoras is considered the 'father of mathematics' and music, known for discovering the mathematical principles of musical harmony.

  • What is the golden ratio?

    The golden ratio is a mathematical ratio often found in nature, associated with beauty and harmony in art and architecture.

  • How does mathematics apply to music?

    Mathematics applies to music through the relationship of string lengths and musical tones, as demonstrated by Pythagoras' discoveries.

  • What role does math play in games?

    Math plays a role in games by providing the geometric framework and strategies, as seen in chess and billiards.

  • How is the golden rectangle significant?

    The golden rectangle is admired for its beautiful proportions and is found in classical architecture and nature.

  • What did Galileo say about mathematics?

    Galileo stated that 'mathematics is the alphabet with which God has written the universe.'

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الترجمات
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التمرير التلقائي:
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    thank you
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    strange
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    okay creature
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    foreign
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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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    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]
  • 00:19:29
    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]
  • 00:24:13
    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]
  • 00:26:04
    the Mind Knows No Limits when used
  • 00:26:06
    properly
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    think of a pentagram Donald
  • 00:26:13
    now put another inside a third
  • 00:26:16
    and a fourth no pencil is sharp enough
  • 00:26:19
    to draw as fine as you can think
  • 00:26:21
    and no paper large enough to hold your
  • 00:26:24
    imagination
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    in fact it is only in the mind that we
  • 00:26:28
    can conceive Infinity
  • 00:26:31
    mathematical thinking has opened the
  • 00:26:33
    doors to the exciting Adventures of
  • 00:26:36
    science
  • 00:26:36
    [Music]
  • 00:26:43
    each Discovery leads to many others an
  • 00:26:47
    endless chain
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    of course they are locked these are the
  • 00:26:59
    doors of the future and the key is
  • 00:27:02
    bottles right
  • 00:27:05
    mathematics the boundless Treasures of
  • 00:27:08
    science are locked behind those doors
  • 00:27:11
    in time they will be opened by the
  • 00:27:13
    curious and inquiring minds of future
  • 00:27:15
    Generations
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    in the words of Galileo
  • 00:27:21
    mathematics is the alphabet with which
  • 00:27:24
    God has written the universe
  • 00:27:26
    [Music]
الوسوم
  • Pythagoras
  • Music
  • Mathematics
  • Golden Ratio
  • Geometry
  • Nature
  • Architecture
  • Games
  • Beauty
  • Science