Engineering topics

Apostol, Tom M.

Publications and source records attributed to Apostol, Tom M..

7 records

NASA NTRS1995

The Tunnels of Samos

This 'Project Mathematics' series video from CalTech presents the tunnel of Samos, a famous underground aquaduct tunnel located near the capital of Pithagorion (named after the famed Greek mathematician, Pythagoras, who lived there), on one of the Greek islands. This tunnel was constructed around 600 BC by King Samos and was built under a nearby mountain. Through film footage and computer animation, the mathematical principles and concepts of why and how this aquaduct tunnel was built are explained.

Apostol, Tom M.↗

NASA NTRS1994

Sines and Cosines. Part 3 of 3

In this 'Project Mathematics' series video, the addition formulas of sines and cosines are explained and their real life applications are demonstrated. Both film footage and computer animation is used. Several mathematical concepts are discussed and include: Ptolemy's theorem concerned with quadrilaterals; the difference between a central angle and an inscribed angle; sines and chord lengths; special angles; subtraction formulas; and a application to simple harmonic motion. A brief history of the city Alexandria, its mathematicians, and their contribution to the field of mathematics is shown.

Apostol, Tom M.↗

NASA NTRS1993

Sines and Cosines. Part 2 of 3

The Law of Sines and the Law of Cosines are introduced and demonstrated in this 'Project Mathematics' series video using both film footage and computer animation. This video deals primarily with the mathematical field of Trigonometry and explains how these laws were developed and their applications. One significant use is geographical and geological surveying. This includes both the triangulation method and the spirit leveling method. With these methods, it is shown how the height of the tallest mountain in the world, Mt. Everest, was determined.

Apostol, Tom M.↗

NASA NTRS1992

Sines and Cosines. Part 1 of 3

Applying the concept of similarities, the mathematical principles of circular motion and sine and cosine waves are presented utilizing both film footage and computer animation in this 'Project Mathematics' series video. Concepts presented include: the symmetry of sine waves; the cosine (complementary sine) and cosine waves; the use of sines and cosines on coordinate systems; the relationship they have to each other; the definitions and uses of periodic waves, square waves, sawtooth waves; the Gibbs phenomena; the use of sines and cosines as ratios; and the terminology related to sines and cosines (frequency, overtone, octave, intensity, and amplitude).

Apostol, Tom M.↗

NASA NTRS1991

Polynomials

In this 'Project Mathematics! series, sponsored by California Institute for Technology (CalTech), the mathematical concept of polynomials in rectangular coordinate (x, y) systems are explored. sing film footage of real life applications and computer animation sequences, the history of, the application of, and the different linear coordinate systems for quadratic, cubic, intersecting, and higher degree of polynomials are discussed.

Apostol, Tom M.↗

NASA NTRS1990

Similarity

In this 'Project Mathematics! series, sponsored by the California Institute for Technology (CalTech), the mathematical concept of similarity is presented. he history of and real life applications are discussed using actual film footage and computer animation. Terms used and various concepts of size, shape, ratio, area, and volume are demonstrated. The similarity of polygons, solids, congruent triangles, internal ratios, perimeters, and line segments using the previous mentioned concepts are shown.

Apostol, Tom M.↗

NASA NTRS1989

The Story of PI

The early history and the uses of the mathematical notation - pi - are presented through both film footage and computer animation in this 'Project Mathematics' series video. Pi comes from the first letter in the Greek word for perimeter. Archimedes, and early Greek mathematician, formulated the equations for the computation of a circle's area using pi and was the first person to seriously approximate pi numerically, although only to a few decimal places. By 1985, pi had been approximated to over one billion decimal places and was found to have no repeating pattern. One use of pi is the application of its approximation calculation as an analytical tool for determining the accuracy of supercomputers and software designs.

Apostol, Tom M.↗