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Convergence articles

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But What's in the Flasks?

Thirty flasks—10 full, 10 half-empty, and 10 completely empty—are to be divided among 3 sons so that flasks and contents should be shared equally. How may this be done?

Circle With a Chord

In a circle whose circumference is 60 units, a chord is drawn forming a segment whose sagitta is 2 units. What is the length of the chord?

Diameter of the Earth

The highest point of the Andes is about 4 miles above sea level.

The Ruins of Persepolis

There are two columns in the ruins of Persepolis left standing upright; one is 70 ft. above the plane, and the other 50 ft;

SMURCHOM: Providing Opportunities for Undergraduate Research in the History of Mathematics
A description of a long-running conference in which undergraduate mathematics students gather to share their research on the history of mathematics.
The Host Riding Horseback

A guest on horseback rides 300 li in a day. The guest leaves his clothes behind and the host rides off to catch up with the guest once he discovers the clothes. Assuming the host rides without stop tell how far he can go in a day?

Triangles in the Sky: Trigonometry and Early Theories of Planetary Motion
A survey of early theories of planetary motion, with dynamic figures to help in understanding these motions.
Sides of a Rectangle

Given a rectangle, find the line through one vertex of minimum length that passes through the extensions of the two opposite sides.

Equal Surface and Volume

What will the diameter of a sphere be, when its volume and surface area are expressed by the same number?

The Great Calculation According to the Indians, of Maximus Planudes
A translation of part of a thirteenth century work by the Byzantine monk Maximus Planudes on the Hindu-Arabic numerals and the algorithms for calculation.

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