From 8bf12e4949e905f67594d9cb069e69d617b42126 Mon Sep 17 00:00:00 2001 From: Charlie Root Date: Fri, 27 Feb 2026 21:15:23 -0300 Subject: [PATCH] An attempt at solving the space picture problem. --- calculus.pdf | Bin 817199 -> 842402 bytes calculus.tex | 23 ++++++++++++----------- 2 files changed, 12 insertions(+), 11 deletions(-) diff --git a/calculus.pdf b/calculus.pdf index 25fd59d01b5cb9ffdb2b92197049f8f453092e93..97c029b113308b9edf7094c296fc35b56247ca90 100644 GIT binary patch delta 253605 zcmV(=K-s^q@G+vbGq6?>0Wp_xstGB78Ov_uxbZ$;(ML6Qq~TMP66|3%m{}k>B*^-< z&Oz>$JqlWqM`}3>e|_pjwbYiKHG;JdBum9&y{pJpyN8|H{ro}6_|wgYPhV}=X`Pkc zo88U*F1J~3i(RlLE6d%@arbNTeX6>>3CX$Nr`F`j<35E|KkWZ?^Vd&beYxC!u3eE8 zWxh+b%bd%ZfMLwsFENYEs}i^%j9aDj7CE1lp@>LY2_3Zy09Tq0)LBsZ&Sj;Q(>4i( z%ogP?U7-B{QWz7l*Sr~(nV|m&=G42GbN?T6;hoIccQI#QWzPH&%ta?MOF}LKM_n=Z zXGU8)b!xTG3Ye$BUug`Z9&2`g>!D`9?x*umjXbY^dmQR)~mSyz=sK5ZXsPMJL0dqL2mVmqLht-X`KC*A(4F z(gPblvH{RzEh9=-1GVRm00=s1MoJ6t2{vc~sz}U$K8!k4<4okxwABfK8hH0kC%*_; 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-277,7 +277,7 @@ O caso mais complicado é quando o subtraendo não é menor que o minuendo, que é o que ocorre em $37 - 19$, ilustrado pela Figura~\ref{fg-alkw-diff}. -\begin{figure}[H] +\begin{figure}[!htb] \centering \begin{verbatim} 37 20 + 17 @@ -311,7 +311,7 @@ representam o número $6440 = 322 \times 20$, mas tipicamente omiti-se o zero já que $322 \times 20 = 322\times 2 \times 10$ e multiplicação por dez é trivial. -\begin{figure}[H] +\begin{figure}[!htb] \centering \begin{verbatim} 322 @@ -337,7 +337,7 @@ soma envolvendo nove termos, cada um deles com nove algarismos --- sugerindo um crescimento quadrático do volume de trabalho da multiplicação convencional, isto é, da multiplicação de \al. -\begin{figure}[H] +\begin{figure}[!htb] \centering \begin{verbatim} (*) A multiplicação de 123456789 por 987654321 @@ -390,7 +390,7 @@ que é 1 ---, teríamos marcado um {\tt x} só nos algarismos {\tt 123456}, indicando que ainda consideraremos os algarismos {\tt 789123456789} ao longo da computação do algoritmo. -Por que se chama divisão longa? Pra ser constrastada com divisão +Por que se chama divisão longa? Pra ser distinguida com divisão curta. Na divisão longa, escrevemos a multiplicação parcial do quociente pelo divisor logo abaixo do dividendo parcial; em seguida, efetuamos a subtração. Na divisão curta, omitimos a subtração tal que @@ -400,9 +400,10 @@ Figura~\ref{fg-alkw-long-div} (na página \pageref{fg-alkw-long-div}), desenhamos uma seta indicando o produto do algarismo corrente do quociente (corrente durante a execução do algoritmo) que deu origem ao minuendo. Assim, o quociente escrito abaixo do divisor poderia ser -omitido da Figura~\ref{fg-alkw-long-div}. +omitido da Figura~\ref{fg-alkw-long-div} (na +página~\pageref{fg-alkw-long-div}). -\begin{figure}[H] +\begin{figure}[!htb] \centering \begin{verbatim} (*) A divisão de 123456789123456789 por 123123 @@ -460,13 +461,13 @@ omitido da Figura~\ref{fg-alkw-long-div}. \end{figure} \begin{figure}[!htb] - \centering + \centering\small \begin{verbatim} (*) A tabela de multiplicação por 123123 -| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | -|--------+--------+--------+--------+--------+--------+--------+--------+---------| -| 123123 | 246246 | 369369 | 492492 | 615615 | 738738 | 861861 | 984984 | 1108107 | + | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | + |------+------+------+------+------+------+------+------+-------| + |123123|246246|369369|492492|615615|738738|861861|984984|1108107| \end{verbatim} \caption{Uma base de dados útil à divisão por 123123. Sem ela, precisaríamos buscar cada algarismo do quociente a cada etapa,