Knowledge about historical mathematics, nested patterns, number theory and representations of numbersNicomachus's theorem states that 1^3 + 2^3 + ... + n^3 = (1 + 2 + ... + n)^2, where n is a positive integer. In words, the sum of the cubes from 1 to n is equal to the square of the sum from 1 to n. For a visual proof, calculate the total area in the figure in two different ways: First, count the unit squares from the center to an edge to get 1 + 2 + 3 + ... + n, so that the total area is 4(1 + 2 + ... + n)^2. Second, consider that each square ring consists of 4k squares of side k, with area 4k^3Componente Curricular::Ensino Fundamental::Séries Finais::Matemática