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Logarithms: The Early History of a Familiar Function

The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.

The Amount of Time a Man Can Do Work

How long does it take a single man to do work when...

Pennies for the Poor

If I were to give 7 pennies to each beggar at my door, I would have 24 pennies left in my purse. How many beggars are there and how much money do I have?

Contractors

A carpenter has undertaken to build a house in 20 days. He takes on another man and says; "If we build the house together, we can accomplish the work in 8 days!" How long would it take this other man to build the house working alone?

An Inscribed Ellipse

Given right triangle ABC where C is the right angle, ellipse O (a,b) is inscribed in it, with its major axis parallel to BC. Calculate the semi-major axis, a, in terms of AC, BC and b.

Lucky Seven

There is a number which when divided by 2, or 3, or 4, or 5, or 6, always has a remainder of 1, and is truly divisible by 7. It is sought what is the number.

Two Equal Parts of a Triangle

The three sides of a triangular piece of land, taken in order, measure 15, 10, and 13 chains respectively.

Integral Pounds

A certain man had in his trade four weights with which he could weigh integral pounds from one up to 40. How many pounds was each weight?

HOM SIGMAA 2011 Student Paper Contest Winners

Download the three winning essays to learn about Kepler's mathematical astronomy, the roots of modern algebra, and the Quadrivium of Isidore of Seville.

A Room with a View

Find the height of a window.