#### Filter Results:

- Full text PDF available (19)

#### Publication Year

2002

2015

- This year (0)
- Last 5 years (3)
- Last 10 years (8)

#### Publication Type

#### Co-author

#### Journals and Conferences

Learn More

- Tom M. Apostol, Mamikon A. Mnatsakanian
- The American Mathematical Monthly
- 2003

1. INTRODUCTION. Given a finite set of fixed points in 3-space, what is the lo-cus of a point moving in such a way that the sum of the squares of its distances from the fixed points is constant? The… (More)

- Tom M. Apostol, Mamikon A. Mnatsakanian
- The American Mathematical Monthly
- 2004

1. INTRODUCTION. A spectacular landmark in the history of mathematics was the discovery by Archimedes (287-212 B.C.) that the volume of a solid sphere is two-thirds the volume of the smallest… (More)

- Tom M. Apostol, Mamikon A. Mnatsakanian
- The American Mathematical Monthly
- 2006

1. INTRODUCTION. Although it is well known that every tetrahedron circum-scribes a sphere, the following two simple consequences apparently have not been previously recorded. First, any plane through… (More)

- Tom M. Apostol, Mamikon A. Mnatsakanian
- The American Mathematical Monthly
- 2010

The classical involute of a plane base curve intersects every tangent line at a right angle. This paper introduces a tanvolute, which intersects every tangent line at any given fixed angle. This… (More)

- Tom M. Apostol, Mamikon A. Mnatsakanian
- The American Mathematical Monthly
- 2007

Now imagine the elliptical cross section replaced by any curve lying on the surface of a right circular cylinder. What happens to this curve when the cylinder is unwrapped? Consider also the inverse… (More)

In earlier work ([1]-[5]) the authors used the method of sweeping tangents to calculate area and arclength related to certain planar regions. This paper extends the method to determine volumes of… (More)

- Tom M. Apostol, Mamikon A. Mnatsakanian
- The American Mathematical Monthly
- 2004

1. INTRODUCTION. The centroid of the boundary of an arbitrary triangle need not be at the same point as the centroid of its interior. But we have discovered that the two centroids are always… (More)

- Tom M. Apostol, Mamikon A. Mnatsakanian
- The American Mathematical Monthly
- 2002

1. MAMIKON’S THEOREM. Areas and volumes of many classical regions can be determined by an intuitive geometric method that does not require integral calculus or even equations for the boundaries. The… (More)

- T. W. Gamelin, Mamikon A. Mnatsakanian
- 2005

Our goal is to study Pascal-Sierpinski gaskets, which are certain fractal sets defined in terms of divisibility of entries in Pascal’s triangle. The principal tool is a “carry rule” for the addition… (More)