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Convergence articles

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Conic Contents

Determine the greatest cylinder that can be inscribed in a given cone.

Tree and Vine

A tree is 2 zhang tall and has a circumference of 3 chi. There is a vine that winds seven equally spaced times around the tree and reaches the top. What is the length of the vine?

Lotus in the Lake

In a certain lake, swarming with red geese, the tip of a lotus bud was seen to extend a span above the surface of the water.

Two Numbers

Find two numbers with sum 20 and when squared their sum is 208.

Sick Leave

A teacher agreed to teach 9 months for $562.50 and his board. At the end of the term, on account of two months' absence caused by sickness, he received only $409.50. What was his board worth per month?

A Disquisition on the Square Root of Three
The author compares Greek ladder, continued fraction, and Newton's Method approximations, noting that the Greek ladder easily gives both of Archimedes' famous bounds.
The Length of a String

Two circles, the sum of whose radii is a, are placed in the same plane with their centers at a distance 2a...

Introducing the History of Mathematics: An Italian Experience Using Original Documents

A discussion of a collaborative effort in Italy to produce materials enabling secondary school teachers to use the history of mathematics in the classroom.

Inscribed Circle

Given: a circle with an inscribed equilateral triangle. The triangle has sides which are 12 cubits long. What is the area of the circle?

Doing Some Gardening

There is a garden is the shape of a rhombus whose side is 577.5 feet. Within the garden is an inscribed square flower bed whose side is 396 feet. What is the area of the garden?

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