\( \newcommand{\abcp}[3]{\frc{#1+\sqrt{#2}}{#3}} \newcommand{\chao}[1]{\left\lfloor #1 \right\rfloor } \newcommand{\nPr}[2]{{}^{#1}A_{#2} } \newcommand{\combin}[2]{{}^{#1}C_{#2} } \newcommand{\cmod}[3]{#1 \equiv #2\left(\bmod {}{#3}\right)} \newcommand{\frc}[2]{\displaystyle\frac{#1}{#2}} \newcommand{\mdc}[2]{\left( {#1},{#2}\right)} \newcommand{\mmc}[2]{\left[ {#1},{#2}\right]} \newcommand{\cis}{\mathop{\rm cis}} \newcommand{\ImP}{\mathop{\rm Im}} \newcommand{\ReP}{\mathop{\rm Re}} \newcommand{\sen}{\mathop{\rm sen}} \newcommand{\tg}{\mathop{\rm tg}} \newcommand{\cotg}{\mathop{\rm cotg}} \newcommand{\cosec}{\mathop{\rm cosec}} \newcommand{\cotgh}{\mathop{\rm cotgh}} \newcommand{\cosech}{\mathop{\rm cosech}} \newcommand{\sech}{\mathop{\rm sech}} \newcommand{\sh}{\mathop{\rm sh}} \newcommand{\ch}{\mathop{\rm ch}} \newcommand{\th}{\mathop{\rm th}} \newcommand{\senEL}[1]{\mathop{\rm sen}^{#1}} \newcommand{\tgEL}[1]{\mathop{\rm tg}^{#1}} \newcommand{\cotgEL}[1]{\mathop{\rm cotg}^{#1}} \newcommand{\cosecEL}[1]{\mathop{\rm cosec}^{#1}} \newcommand{\shEL}[1]{\mathop{\rm sh^{#1}}} \newcommand{\chEL}[1]{\mathop{\rm ch^{#1}}} \newcommand{\thEL}[1]{\mathop{\rm th^{#1}}} \newcommand{\cotghEL}[1]{\mathop{\rm cotgh^{#1}}} \newcommand{\cosechEL}[1]{\mathop{\rm cosech^{#1}}} \newcommand{\sechEL}[1]{\mathop{\rm sech^{#1}}} \newcommand{\senq}{\senEL{2}} \newcommand{\tgq}{\tgEL{2}} \newcommand{\cotgq}{\cotgEL{2}} \newcommand{\cosecq}{\cosecEL{2}} \newcommand{\cotghq}{\cotghEL{2}} \newcommand{\cosechq}{\cosechEL{2}} \newcommand{\sechq}{\sechEL{2}} \newcommand{\shq}{\shEL{2}} \newcommand{\chq}{\chEL{2}} \newcommand{\arctg}{\mathop{\rm arctg}} \newcommand{\arcsen}{\mathop{\rm arcsen}} \newcommand{\argsh}{\mathop{\rm argsh}} \newcommand{\argch}{\mathop{\rm argch}} \newcommand{\argth}{\mathop{\rm argth}} \newcommand{\Var}{\mathop{\rm Var}} \newcommand{\vect}[1]{\overrightarrow{#1}} \newcommand{\tr}[1]{ \textnormal{Tr}\left({#1}\right)} \newcommand{\C}{\mathbb{C}} \newcommand{\E}{\mathbb{E}} \newcommand{\H}{\mathbb{H}} \newcommand{\I}{\mathbb{I}} \newcommand{\K}{\mathbb{K}} \newcommand{\N}{\mathbb{N}} \newcommand{\P}{\mathbb{P}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\R}{\mathbb{R}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\til}{\sim} \newcommand{\mdc}{\mathop{\rm m.d.c.}} \newcommand{\mmc}{\mathop{\rm m.m.c.}} \newcommand{\vect}[1]{\overrightarrow{#1}} \newcommand{\dfrc}{\displaystyle\frac} \newcommand{\Mod}[1]{\ (\mathrm{mod}\ #1)} \)

domingo, 2 de fevereiro de 2025

Uma surpresa... pouco surpreendente.

 

Hoje, vi este vídeo pela primeira vez no youtube.

Os meus ex-alunos que têm uma casio fx-9860G (ou alguma das suas variantes), têm um programa com gráficos 3D, criado por mim que usa as ideias matemáticas por detrás ... daquilo!

 Mas há um detalhe. Eu não li nem aprendi essas ideias. Deduzi-as eu!

Hoje em dia, jogo Elite Dangerous: https://youtube.com/playlist?list=PL89Mp6mqi5UqwT-U7AeBwk61iX3wICWFx&si=j-sGoPB87vDWxPYf

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