中級 989 タグ追加 保存
動画の字幕をクリックしてすぐ単語の意味を調べられます!
単語帳読み込み中…
字幕の修正報告
One, two, three, four, five, six, seven, eight, nine, and zero.
With just these ten symbols, we can write any rational number imaginable.
But why these particular symbols?
Why ten of them?
And why do we arrange them the way we do?
Numbers have been a fact of life throughout recorded history.
Early humans likely counted animals in a flock or members in a tribe
using body parts or tally marks.
But as the complexity of life increased, along with the number of things to count,
these methods were no longer sufficient.
So as they developed,
different civilizations came up with ways of recording higher numbers.
Many of these systems,
like Greek,
Hebrew,
and Egyptian numerals,
were just extensions of tally marks
with new symbols added to represent larger magnitudes of value.
Each symbol was repeated as many times as necessary and all were added together.
Roman numerals added another twist.
If a numeral appeared before one with a higher value,
it would be subtracted rather than added.
But even with this innovation,
it was still a cumbersome method for writing large numbers.
The way to a more useful and elegant system
lay in something called positional notation.
Previous number systems needed to draw many symbols repeatedly
and invent a new symbol for each larger magnitude.
But a positional system could reuse the same symbols,
assigning them different values based on their position in the sequence.
Several civilizations developed positional notation independently,
including the Babylonians,
the Ancient Chinese,
and the Aztecs.
By the 8th century, Indian mathematicians had perfected such a system
and over the next several centuries,
Arab merchants, scholars, and conquerors began to spread it into Europe.
This was a decimal, or base ten, system,
which could represent any number using only ten unique glyphs.
The positions of these symbols indicate different powers of ten,
starting on the right and increasing as we move left.
For example, the number 316
reads as 6x10^0
plus 1x10^1
plus 3x10^2.
A key breakthrough of this system,
which was also independently developed by the Mayans,
was the number zero.
Older positional notation systems that lacked this symbol
would leave a blank in its place,
making it hard to distinguish between 63 and 603,
or 12 and 120.
The understanding of zero as both a value and a placeholder
made for reliable and consistent notation.
Of course, it's possible to use any ten symbols
to represent the numerals zero through nine.
For a long time, the glyphs varied regionally.
Most scholars agree that our current digits
evolved from those used in the North African Maghreb region
of the Arab Empire.
And by the 15th century, what we now know as the Hindu-Arabic numeral system
had replaced Roman numerals in everyday life
to become the most commonly used number system in the world.
So why did the Hindu-Arabic system, along with so many others,
use base ten?
The most likely answer is the simplest.
That also explains why the Aztecs used a base 20, or vigesimal system.
But other bases are possible, too.
Babylonian numerals were sexigesimal, or base 60.
Any many people think that a base 12, or duodecimal system,
would be a good idea.
Like 60, 12 is a highly composite number that can be divided by two,
three,
four,
and six,
making it much better for representing common fractions.
In fact, both systems appear in our everyday lives,
from how we measure degrees and time,
to common measurements, like a dozen or a gross.
And, of course, the base two, or binary system,
is used in all of our digital devices,
though programmers also use base eight and base 16 for more compact notation.
So the next time you use a large number,
think of the massive quantity captured in just these few symbols,
and see if you can come up with a different way to represent it.
コツ:単語をクリックしてすぐ意味を調べられます!

読み込み中…

【TED-Ed】A brief history of numerical systems - Alessandra King

989 タグ追加 保存
黃如育 2017 年 1 月 22 日 に公開
お勧め動画

コメント

読み込み中…
  1. 1. クリック一つで単語を検索

    右側のスプリクトの単語をクリックするだけで即座に意味が検索できます。

  2. 2. リピート機能

    クリックするだけで同じフレーズを何回もリピート可能!

  3. 3. ショートカット

    キーボードショートカットを使うことによって勉強の効率を上げることが出来ます。

  4. 4. 字幕の表示/非表示

    日・英のボタンをクリックすることで自由に字幕のオンオフを切り替えられます。

  5. 5. 動画をブログ等でシェア

    コードを貼り付けてVoiceTubeの動画再生プレーヤーをブログ等でシェアすることが出来ます!

  6. 6. 全画面再生

    左側の矢印をクリックすることで全画面で再生できるようになります。

  1. クイズ付き動画

    リスニングクイズに挑戦!

  1. クリックしてメモを表示

  1. UrbanDictionary 俚語字典整合查詢。一般字典查詢不到你滿意的解譯,不妨使用「俚語字典」,或許會讓你有滿意的答案喔