Convergence articles

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Limit Points and Connected Sets in the Plane

A study of Mullikan's Nautilus, using movies to illustrate the important ideas

A square walled city of unknown dimensions has four gates, one at the center of each side.

A man plants 4 kernels of corn, which at harvest produce 32 kernels: these he plants the second year; now, supposing the annual increase to continue 8 fold, what would be the produce of the 15th year, allowing 1000 kernels to a pint?

Peano on Wronskians: A Translation

How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students

Squared Proof

Prove that if the sums of the squares of opposite sides of any quadrilateral are equal, its diagonals intersect at right angles.

Al-Khwarizmi's Algebra

Page from al-Khwarizmi's algebra text written in about 825. The proof of the rule for solving a quadratic equation of the form "squares plus roots equal numbers".

Four Colors Suffice

The history of the four color problem with sketches of the attempted proofs in the nineteenth century and an outline of the computer proof of the twentieth century.

The Poincare Conjecture: In Search of the Shape of the Universe

The history of the Poincare conjecture up to its recent proof by Grigori Perelman.

History of Mathematics Archive

A wide-ranging website with links to many sources in the history of mathematics.

Inscribed Square

Knowing the base, b, and the altitude, a, of a triangle, find the expression for a side of the inscribed square.