Page 14: Erdos to Foias

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Page 14: Erdos to Foias

I have two fields of grain. From the first field I harvest 2/3 a bushel of grain/unit area; from the second, 1/2 bushel/unit area.

In how many ways can a vowel and a consonant be chosen out of the word "logarithms?"

This is the title page of the Nova Scientia (1537) of Niccolo Tartaglia (1499-1557). In this work, Tartaglia discussed the mathematics of artillery and developed methods for determining the range of a cannon.

On an expedition to seize his enemy's elephants, a king marched 2 yojanas the first day.

A series of circles have their centers on an equilateral hyperbola and pass through its center. Show that their envelope is a lemniscate.

Two persons sat down to play for a certain sum of money; and agree that the first who gets three games shall be the winner. After a few games they resolve to divide the stakes. How much should each person receive?

Prove geometrically that the hypocycloid is a straight line when the radius of the rolling circle is one-half the radius of the fixed circle.

Given two circles tangent to each other and to a common line, determine a relationship between the radii and the distance between the tangent points.

Given the frustum of a circular cone with height h.