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Rectangular prisms
No full textTo calculate the volume of a rectangular prism all you need to do is take the product of length, width, and height. The surface area is slightly more complex, and is equal to 2×length×width + 2×length×height + 2×width×height. The total edge length is 4×(length + width + height)Componente Curricular::Ensino Fundamental::Séries Finais::Matemátic
Sendov's conjecture
No full textKnowlegde about complex analysis, derivatives and polynomialsMade by Blagovest Sendov circa 1958, this conjecture has eluded proof despite a heated interest among many mathematicians. It states simply that for a polynomial f(z)=(z-r1)(z-r2)...(z-rn) with n>=2 and each root rk located inside the closed unit disk |z|<=1 in the complex plane, it must be the case that every closed disk of radius 1 centered at a root will contain a critical point of f. Since the Lucas–Gauss theorem implies that the critical points of f must themselves lie in the unit disk, it seems completely implausible that the conjecture could be false. Yet, at present, it has not been proven for polynomials with real coefficients or for any polynomial whose degree exceeds 8.
Set the degree of the polynomial (i.e., the number of roots) using the popup menu. Initially, the polynomial f(z)=z^n-1 is used, so that the roots are the n^(th) roots of unity. The roots of f are blue locators; simply drag a root to change its value. The critical points of f (the roots of the derivative) are shown in orange. Sendov's conjecture will be disproved if you can manipulate things in such a way that there is a disk that does not contain an orange pointComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemátic
Reverse collatz paths
No full textKnowledge about algorithms, integers, number theory and recursionThe Collatz conjecture states that repeating the following algorithm starting with any positive integer n eventually reaches the number 1.
n={(n/2) if n is even or (3n+1) if n is odd}
Running the Collatz algorithm in reverse starting at 1 creates a graph. The Collatz conjecture is equivalent to saying that this graph contains every positive integerComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemátic
Distributions of leading digits
No full textKnowledge about number theoryMany sequences have the property that the distribution of their leading digits converges to a definite distribution. Check out a few sequences, and note that not all of them converge to the same distributionComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemátic
The 3n+1 problem
No full textKnowledge about algorithms, discrete mathematics and number theoryStart with a number. Then at each step, if n is even, compute n/2, and if n is odd, compute 3n+1. So far as anyone can tell, the resulting sequence always eventually reaches 1. But despite work since the 1930s, no proof is knownComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemátic
Newton's rotating bucket experiment
No full textIn the Scholium to Book 1 of Principia, Isaac Newton describes an experiment in which a bucket of water hung by a long cord is twisted and released. Initially, only the bucket rotates while the water remains stationary, as indicated by its flat surface. Gradually, the rotational motion is communicated to the water and centrifugal force distorts its surface into a paraboloid. After the bucket stops turning, the water continues to rotate until frictional forces again bring it to rest, flattening the paraboloid. (Viscosity, which causes this friction, is described by another law proposed by Newton!) Newton cited the rotating-bucket experiment to support his notion of absolute space as the reference frame for all motion. His contemporary Leibniz challenged Newton's worldview, arguing that space is actually created by the existence of material bodies. This debate continued into the twentieth century, principally associated with the writings of Mach and Einstein, and providing a philosophical underpinning for the general theory of relativity (see reference in Details).
This Demonstration is intended to be only qualitatively descriptiveComponente Curricular::Ensino Médio::Físic
Alexander the Great 11 - deterioration of character
No full textIt is necessary to have some prior knowledge in EnglishThis audio is a story about the most briliant military commander Alexander the Great. He was a very important person in Greeks historyComponente Curricular::Ensino Fundamental::Séries Finais::Língua EstrangeiraComponente Curricular::Ensino Médio::Língua EstrangeiraComponente Curricular::Ensino Médio::LiteraturaComponente Curricular::Educação Superior::Linguística, Letras e Artes::LinguísticaComponente Curricular::Educação Superior::Linguística, Letras e Artes::Letra
Saúde ocupacional e meio ambiente
No full textEste vídeo aborda as doenças causadas pelo trabalho moderno e aparentemente mecanizado, porém, sem abrir mão do ser humano, que parece sofrer mais ainda nos dias de hoje, esquecendo os limites entre a segurança e o perigoComponente Curricular::Ensino Fundamental::Séries Finais::Meio Ambient
Propagação da Luz
No full textAtravés de três alfinetes alinhados em uma placa de isopor, observa-se que a luz propaga-se em linha retaComponente Curricular::Ensino Médio::Físic
Finite limit at a finite point
No full textDefinition of limit of a function with epsilons and deltasThis Demonstration computes the largest delta1 and delta2 for a given epsilon so that f(x) lies between L-epsilon and L+epsilonComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemátic