Uma BREVE HISTÓRIA da MEDIDA e da INTEGRAÇÃO

➡️ Learn real Calculus, starting from scratch (pre-calculus) to advanced level! Click here and join Mastering Calculus: https://www.temciencia.com.br What does it really mean to measure something? In this video, we'll discuss the history of the measure of integration, from the most basic idea of measuring a length with a ruler, through the discovery of incommensurables by the Pythagoreans, the invention of calculus in a not entirely rigorous form by Newton and Leibniz, the theoretical refinements of calculus and analysis in the following centuries, the Riemann integral, the Lebesgue integral, and the Banach-Tarski paradox. A brief history covering more than two thousand years of human thought, at increasingly abstract levels. Become a member and help me continue producing this type of content: https://www.youtube.com/temciencia/join ========================================== Script, presentation, and editing: Daniel Nunes My Instagram:   / tem.ciencia   ===================================== WATCH ALSO: 🔴 POINCARÉ CONJECTURE: A MILLION DOLLAR Problem    • CONJECTURA DE POINCARÉ: um problema de 1 M...   🔴 ARISTOTLE'S WHEEL PARADOX    • O PARADOXO DA RODA DE ARISTÓTELES   🔴 ARE YOU RATIONAL? (Allais' Paradox and Prospect Theory)    • VOCÊ É RACIONAL? (Paradoxo de Allais e a T...   🔴 THE BIRTHDAY PARADOX    • O PARADOXO DO ANIVERSÁRIO (como você nunca...   🔴 PRISONERS' DILEMMA and NASH'S EQUILIBRIUM    • DILEMA dos PRISIONEIROS e o EQUILÍBRIO de ...   🔴 ST. PETERSBURG PARADOX: HOW MUCH IS INFINITE MONEY WORTH?    • PARADOXO DE SÃO PETERSBURGO: QUANTO VALE D...   🔴 Math and Sports Betting: HOW TO BREAK THE BANK?    • Matemática e Apostas Esportivas: COMO QUEB...   🔴 THE (Almost) IMPOSSIBLE PROBLEM | The 3-House Problem    • O PROBLEMA (quase) IMPOSSÍVEL | Problema d...   🔴 WHY (Scientifically) THERE IS NO SCIENTIFIC PROOF    • POR QUE (cientificamente) NÃO EXISTE COMPR...   🔴 Was Mathematics Discovered or Invented?    • A MATEMÁTICA foi DESCOBERTA ou INVENTADA?   🔴 WHY IS CALCULUS SO HARD?    • POR QUE CÁLCULO É TÃO DIFÍCIL? (Ou não)   🔴 WHAT IS IT LIKE TO GET A DOCTORATE IN MATHEMATICS AT IMPA    • COMO É FAZER UM DOUTORADO EM MATEMÁTICA NO...   🔴 HOW IS THE ENEM SCORE ACTUALLY CALCULATED?    • TRI: a MATEMÁTICA por trás da NOTA do ENEM   🔴 PageRank: HOW GOOGLE's Mathematical Algorithm Works    • PageRank: COMO funciona o ALGORITMO Matemá...   🔴 A GAME NOBODY CAN WIN. Here's why.    • Um JOGO que NINGUÉM CONSEGUE VENCER. Eis o...   🔴 WHY DO YOU HAVE FEWER FRIENDS than your friends?    • POR QUE VOCÊ tem MENOS AMIGOS que os seus ...   🔴 THE ILLUSION of MAJORITY    • A ILUSÃO da MAIORIA   🔴 THE HARDEST QUESTION IN THE HISTORY OF GOOGLE    • A QUESTÃO MAIS DIFÍCIL DA HISTÓRIA DO GOOGLE   🔴 WHAT IS MATHEMATICS FOR? When will you actually use it?    • PRA QUE serve a MATEMÁTICA? Quando você ir...   🔴 WOULD YOU PASS AN INTERVIEW with AMAZON? AND MICROSOFT?    • VOCÊ PASSARIA numa ENTREVISTA da AMAZON? E...   🔴 THE PROBLEM with VOLUME FORMULAS that INTRUSTED GAUSS    • O GRANDE PROBLEMA com as FÓRMULAS de VOLUME   🔴 WHY are there only 5 PLATONIC SOLIDS in 3D?    • POR QUE só existem 5 SÓLIDOS DE PLATÃO em 3D?   🔴 What is NON-EUCLIDEAN GEOMETRY? - History of Geometry    • O que é GEOMETRIA NÃO EUCLIDIANA? - Histór...   🔴 THE RING PARADOX    • O PARADOXO DO ANEL   🔴 The SECRET Math of Things    • Onde está a Matemática Avançada no nosso d...   🔴 HOW WAS PI CALCULATED (with a matchbox)?    • COMO CALCULAR o PI arremessando FÓSFOROS? ...   🔴 3 PARADOXES OF INFINITY    • 3 PARADOXOS DO INFINITO   🔴 Hilbert's INFINITY Hotel: How to Count Infinity?    • O Hotel INFINITO de Hilbert: um PARADOXO d...