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Convergence articles

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An Investigation of Historical Geometric Constructions

Dynamic geometry software is used to demonstrate early Greek attempts at the trisection of an angle and the squaring of a circle.

Dimensions of a Triangle

Determine the dimensions for a right-angled triangle, having been given the hypotenuse, and the side of the inscribed square.

Investigating Euler's Polyhedral Formula Using Original Sources

The author shows how teachers can use Leonhard Euler's original works in the classroom to explore Euler's famous polyhedral formula,
V + F = E + 2.

Travelling Steamers

The steamer, Katie, leaves the wharf at New Orleans and runs an average speed of 15 mph. When Katie had gone 25 miles, the steamer R.E. Lee leaves the wharf and runs the average speed of 18 mph. How far will the Lee go before she overtakes the Katie?

Perpendicular Curves

Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.

Numbers Game #1

The sum of two numbers is 10 and their product is 40. What are the numbers?

Unknown Quantity; A Real and Imaginary History of Algebra

A history of algebra from its early beginnings to the twentieth century.

Calculate a Triangle

Having been given the perimeter and perpendicular of a right angled triangle, it is required to find the triangle.

Parallelepiped Chimney

The cavity of our chimney is an upright parallelepiped, the diagonal of whose base is 60"; and the height of the lower side of the lintel above the plane of the floor is 40".

Review of Routes of Learning: Highways, Pathways, and Byways in the History of Mathematics

In this collection of essays on modern trends and issues in the history of mathematics, consideration of mathematics history in the classroom is often more theoretical than practical.

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