# Project Mathematics (7 Parts)

Synopsis
A series of videotape-and-workbook modules that explore basic topics in GCSE and A-level mathematics, using live action, music, special effects, and computer animation. Each module consists of a videotape and workbook.
Language
English
Country
Great Britain
Notes
Video clip extracts are available online at http://www.projectmathematics.com/
Documentation
Each video is accompanied by a workbook
Subjects
Mathematics; FE
Keywords
geometry; trigonometry

### Distribution Formats

Type
VHS
Format
PAL
Price
£35 (each)
Availability
Sale
Duration/Size
22, 28, 26, 24, 28, 29, 29 minutes each
Year
2005

### Sections

Title
Theorem of Pythagoras, The
Synopsis
The video examines Pythagoras’ theorem and emphasizes its use in everyday practical problems. It begins with three real-life versions of the same mathematical problem: how do you find the length of one side of a right triangle if the lengths of the other two sides are known.The problem is solved by a simple computer-animated derivation of the Pythagorean theorem (based on similar triangles).

The algebraic formula a2 + b2 = c2 is interpreted geometrically in terms of areas of squares, and is then used to solve the three real-life problems posed earlier. Historical context is provided through stills showing Babylonian clay tablets and various editions of Euclid’s Elements. Several different computer-animated proofs of the Pythagorean theorem are presented (extending it to 3-dimensional space), and shows how the Pythagorean theorem is used in trigonometry.
Duration
22 mins

Title
Similarity
Synopsis
The video examines similarity and looks at its applications. It is divided into nine sections: shape and size - introduces the concept of similarity; similar triangles - introduces scaling and the scaling factor, and shows how similar triangles have the same shape; applications of similarity - shows how similar triangles can be used to find the height of a column or pyramid; similar polygons and solids; internal ratios for similar figures - shows why any two scaled figures always have the same internal ratos; perimeters of similar figures - shows how perimiters are multiplied by the scaling factor; areas of similar figures - shows how areas are multiplied by the square of the scaling factor; volumes of similar figures - shows how volumes are multiplied by the cube of the scaling factor; applications to biology - explains briefly why a hummingbird’s heart beats faster tan a human’s, and why a praying mantis cannot be enlarged to the size of a horse.
Duration
28 mins

Title
Polynomials
Synopsis
This programme examines polynomials and is divided into six main sections: polynomials in real life - introduces different types and gives examines, including parabolic trajectories and the use of cubic splines in designing sailboats; linear polynomials - shows how their graphs are straight lines of various slopes; quadratic polynomials - shows how their graphs are parabolas (the prototype being the graph of y = x2), animation shows how the Cartesian equation changes when the curve is translated vertically or horizontally or subjected to a vertical change of scale; intersections of lines and parabolas - leads on to zeros of polynomials; cubic polynomials - shows basic properties and discusses possible zeros, local maxima and minima, and points of inflection, explains how there are basically three different cubic curves; polynomials of higher degree - a discussion of quartics and higher degree polynomials, all of which have infinitely many prototypes.
Duration
26 mins

Title
Story of Pi, The
Synopsis
Defines pi as the ratio of circumference to diameter of a circle and shows how pi appears in a variety of formulae. After discussing the early history of pi, the programme invokes similarity to explain why the ratio of circumference to diameter is the same for all circles, regardless of size. This ratio, a fundamental constant of nature, is denoted by the Greek letter pi, so that 2 pi r represents the circumference of a circle of radius r.

Two animated sequences show that a circular disc of radius r can be dissected to form a rectangle of base pi r and altitude r, so the area of the disc is pi r squared, a result known to Archimedes. Animation shows the method used by Archimedes to estimate pi by comparing the circumference of a circle with the perimeters of inscribed and circumscribed polygons.

The next segment describes different rational estimates for pi obtained by various cultures, and points out that pi is irrational. The appearance of pi in probability problem is discussed. The concluding segment explains that major achievements in estimating pi represent landmarks of important advances in the history of mathematics.
Duration
24 mins

Title
Sines and Cosines Part 1: Periodic Functions
Synopsis
The video is divided into five main sections: 1) circular motion and sine waves - introduces the sine in connection with a point moving counter-clockwise on a circle of unit radius, defines a radian, and shows how to plot a sine curve or sine wave; 2) symmetry of sine waves - reveals some basic properties of sine curves, shows how a cosine curve is generated, and discusses relations between sines and cosines; 3) sine waves and sound - shows how a sine wave is generated, introduces frequency and amplitude; 4) periodic waves - emphasises the periodic nature of sine waves, looks at Fourier’s discovery that every periodic wave is a combination of sine and cosine waves with appropriate amplitudes and frequencies, and illustrates this with sine wave approximations to a square wave; 5) sines and cosines as ratios - gives some historical background and shows how sines and cosines occur in triganometry as ratios of the lengths of the sides of right-angled triangles.
Duration
28 mins

Title
Sines and Cosines Part 2: Trigonometry
Synopsis
This video concentrates on triganometry, especially the Cosine Rule and the SiRule. It is divided into seven parts dealing with: 1) trigonometry - looks briefly at its history and current uses in surveying and navigation; 2) sines, cosines and the Pythagorean Theorem - reviews Pythagoras’ Theorem and looks at the trigonometric functions of sines and cosines; 3) the law of cosines - demonstrates the Cosine Rule which relates the lengths of the three sides and one angle of any triangle; 4) applying the law of cosines; 5) the law of sines - demonstrates the Sine Rule which states that in any triangle the sine of an angle divided by the length of the opposite side is constant; 6) applying the law of sines; 7) surveying by triangulation - describes the methods used for surveying by triangulation, including the Great Triganometric Survey of India and determining the height of Mount Everest.
Duration
29 mins

Title
Sines and Cosines Part 3: Addition Formulae
Synopsis
Concentrates on the addition formulae for sines and cosines. Divided into seven parts which deal with: sines and chord lengths; addition formulae for sines; Ptolemy’s theorem on quadilaterals; applications of the addition formulae; sines and cosines of special angles; application to simple harmonic motion; recap of programme.
Duration
29 mins

Name

### Distributor

Name

#### Boulton-Hawker Films Ltd

Email
sales@boultonhawker.co.uk
Web
http://www.boultonhawker.co.uk/ External site opens in new window
Phone
01449 616 200
Fax
01449 677 600