Let's now bring this result into the more modern setting of

coordinate geometry (Fermat and Descartes, 17th century) and linear algebra (Cayley, 19th century) (Burton, 1999).

The first part of the book, six chapters, explains fundamental prerequisite concepts from algebra, geometry,

coordinate geometry, and trigonometry.

Principles and Standards for School Mathematics (NCTM, 2011) Geometry Standard (9-12) * Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships * use trigonometric relationships to determine lengths and angle measures * Specify locations and describe spatial relationships using

coordinate geometry and other representational systems * use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze geometric situations Table 2.

The book is rich in references and allusions to historical topics that Grattan-Guinness has spent a lifetime researching, but at times one wishes he would share more of the wealth of his knowledge to flesh out off-hand comments or bare-bones assertions not readily comprehended by outsiders, such as the claim that Descartes' algebraic geometry was not

coordinate geometry (p.

* A good historical introduction to topics; e.g., you could introduce

Coordinate Geometry through the task "The French Connection from Algebra to Geometry." The brilliant ideas of Descartes have lead us to the amazing GPS (Global Positioning System) technology that we use today.

The investigation involves an analysis of number pattern but also includes work with surds,

coordinate geometry and some elementary use of complex numbers.

The opening chapters walk through the standard procedures for using

coordinate geometry to set up equations, imagining different possibilities, finding ratios or proportions, and determining the number of combinations possible.

The game of Battleship may be used as a context for studying

coordinate geometry. In this classic game, each player has five ships, each of which occupies a certain number of squares on the playing field: the Destroyer (two squares); the Submarine (three squares), the Cruiser (three squares), the Battleship (four squares), and the Aircraft Carrier (five squares).

Platted lot and block information including COGO (

coordinate geometry) metes and bounds attributes for the entire city are now complete.

There is no need to use

coordinate geometry or to calculate end-point locations and angles.

Coverage encompasses problem solving, sets and numeral systems, operations with whole numbers, exponents and estimation, number theory, fractions, decimals, integers, polygons, measurement, transformations,

coordinate geometry, probability, and statistics.

Students should have a solid high school background in algebra and

coordinate geometry. Each chapter includes boxes on connections to other branches of science, engineering, and medicine, and boxed discussions of the physical origins of chemical behavior, along with problems, lab activities, and cumulative exercises.

Prior to learning about trigonometry, students have typically done some basic work on

coordinate geometry and are familiar with gradient as the ratio of "rise over run".

It is essentially a lesson in number pattern but includes work with surds,

coordinate geometry and some elementary use of complex numbers.