Add to ORKGKnowledge 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::Matemátic
We give several ways to derive and express classic summation problems in terms of polycubes. We visu...
Triangular numbers are integers of the form (n²+n)/2; they are 0, 1, 3, 6, 10, 15, 21, 28, …. As a t...
In the third clip in a series of seven from the third of seven interviews in which 8th grader Stepha...
Knowledge about historical mathematics, nested patterns, number theory and representations of number...
Triangular numbers, series, infinit sum, reciprocals of triangular numbers, areaThe sum of the recip...
The graphic is a visual proof that 1+2+3+...+n=(n(n+1))/2 for any positive integer nComponente Curri...
Series, Calculus and Analytic GeometryA series of squares are aligned along the diagonal of a unit s...
We prove a new q analogue of Nicomachus’s theorem about the sum of cubes and some related results. ...
For any two numbers a and b the square of their sum (a+b)² is equal to a² + 2ab + b². You can see a ...
In the fourth clip in a series of six from the second of seven interviews in which 8th grade Stephan...
In words, the square of a sum is the sum of the squares plus twice the cross term. You can see a geo...
Knowledge about number theory and representations of numbersLagrange proved that every positive inte...
In this proof without words, we prove wordlessly the identity 1+3+5+...+(2n-1)=n^2
In this short note, we look for all cases where the sum of a power of 2 and a power of 3 is a per...
A mathematical expression depicting a visual proof that says that alternating some of the first n sq...
We give several ways to derive and express classic summation problems in terms of polycubes. We visu...
Triangular numbers are integers of the form (n²+n)/2; they are 0, 1, 3, 6, 10, 15, 21, 28, …. As a t...
In the third clip in a series of seven from the third of seven interviews in which 8th grader Stepha...
Knowledge about historical mathematics, nested patterns, number theory and representations of number...
Triangular numbers, series, infinit sum, reciprocals of triangular numbers, areaThe sum of the recip...
The graphic is a visual proof that 1+2+3+...+n=(n(n+1))/2 for any positive integer nComponente Curri...
Series, Calculus and Analytic GeometryA series of squares are aligned along the diagonal of a unit s...
We prove a new q analogue of Nicomachus’s theorem about the sum of cubes and some related results. ...
For any two numbers a and b the square of their sum (a+b)² is equal to a² + 2ab + b². You can see a ...
In the fourth clip in a series of six from the second of seven interviews in which 8th grade Stephan...
In words, the square of a sum is the sum of the squares plus twice the cross term. You can see a geo...
Knowledge about number theory and representations of numbersLagrange proved that every positive inte...
In this proof without words, we prove wordlessly the identity 1+3+5+...+(2n-1)=n^2
In this short note, we look for all cases where the sum of a power of 2 and a power of 3 is a per...
A mathematical expression depicting a visual proof that says that alternating some of the first n sq...
We give several ways to derive and express classic summation problems in terms of polycubes. We visu...
Triangular numbers are integers of the form (n²+n)/2; they are 0, 1, 3, 6, 10, 15, 21, 28, …. As a t...
In the third clip in a series of seven from the third of seven interviews in which 8th grader Stepha...