על מנת לערוך סיכומים נדרש לפתוח חשבון.
סיכומונה:ארגז החול: הבדלים בין גרסאות בדף
קפיצה לניווט
קפיצה לחיפוש
אין תקציר עריכה |
אין תקציר עריכה |
||
שורה 1: | שורה 1: | ||
'''Archimedes''' was a [[Greek]] [[mathematician]] who is best known for the myriad mathematical | |||
<math | [[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. | |||
<math | |||