סיכומונה:ארגז החול: הבדלים בין גרסאות בדף

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'''Archimedes''' was a [[Greek]] [[mathematician]] who is best known for the myriad mathematical
[[notation]]s that he invented, most of which are still in use today. His earliest work included
devising simple [[inline equation]]s such as <math>\sin x = \cos^2(y+t)</math> and
<math>x^2 + y^2 = -e^{-\theta}</math>. He pioneered the use of greek symbols such as
<math>\alpha</math> in English writing. While performing complicated calculations such as
<math>\sum_{i=1}^3 i^2 = 47</math>, he noticed that despite the baseline of the equation
lining up nicely with the surrounding text, the so-called [[displayed equation]]
: <math>\displayed\sum_{i=1}^3 i = 46, \qquad \textrm{unless} 46 \not= 47</math>
was probably better value. A similar effect occurred for integrals such as
<math>\int_0^1 \sin^2 x \, dx</math>. He marked this up using the kludgy "\displayed"
command, although he suspected that later and greater thinkers would come up with something
better. When he couldn't make up his mind he would write
: <math>\displayed F(x) = \begin{cases} \left\uparrow\frac{\partial^2 G}{\partial u \partial v}\right\}
& \textrm{if the sky was \bf blue}, \\ A_0 + \cdots + A_k & \textit{if Troy was on the attack.}
\end{cases}</math>
He also invented the polynomial rings <math>\mathbf{R}[x]</math>,
<math>\mathcal{C}[y]</math> and <math>\boldsymbol{\mathcal{C}[z]}</math>, and being
fluent in Chinese he was comfortable writing things like
:<math>\displayed 钱 = \sqrt{不好},</math>
although historians have debated whether his Chinese really was all that good.


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