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Learn about the origins and solutions of cubic equations, which are polynomial equations of degree 3. Explore the contributions of ancient and medieval mathematicians, such as Babylonians, Greeks, Chinese, Indians, and Persians, and the algebraic formula by Ferrari and Cardano.
Learn about the geometry of constructing lengths, angles, and figures using only a ruler and a compass. Find out the history, problems, and methods of this classical technique.
Learn how to count the roots of a polynomial by examining sign changes in its coefficients, as described by René Descartes in his La Géométrie. See examples, proofs, generalizations and related topics.
Learn about the definition, examples, and solution methods of a system of linear equations, a collection of two or more linear equations involving the same variables. Explore the geometric interpretation, the general form, and the behavior of linear systems in different cases.
Wave-particle duality is the concept in quantum mechanics that quantum entities exhibit particle or wave properties according to the experimental circumstances. [1]: 59 It expresses the inability of the classical concepts such as particle or wave to fully describe the behavior of quantum objects. [2]:
The folium of Descartes is an algebraic curve named after René Descartes, who challenged Pierre de Fermat to find its tangent line. Learn about its history, properties, graphing methods, and relation to the trisectrix of Maclaurin.
Learn about the physics theory of three bodies orbiting each other under gravity, and its mathematical description and solutions. Find out the history, applications, and challenges of the three-body problem in classical and quantum mechanics.
A complex number is an expression of the form a + bi, where a and b are real numbers, and i is an imaginary unit. The absolute value (or modulus) of a complex number z is the non-negative square root of the sum of its squares, and the argument of z is the angle from the positive real axis to z.