... numbers and number sense; measurement; patterns and algebra; geometry and statistics and probability. The learning competencies in Numbers and Number Sense are describes and illustrates well-defined sets, subsets, universal set and the null set; defines and describes the union and intersection of sets and the complement of a set; uses Venn Diagrams ... of a line; illustrates, names, identifies and defines the different kinds of angles; derives relationships of geometric figures using measurements and by inductive reasoning: supplementary angles, complementary angles, equal angles, adjac...

• Word Count: 4402
• Approx Pages: 18
• Has Bibliography
• Grade Level: Undergraduate

... prescribed ratio. In On spirals Archimedes defines a spiral. He gives fundamental properties connecting the length of the radius vector with the angles through which it has revolved. He gives results on tangents to the spiral as well as finding the area of portions of the ... rigorous explication and framework, Newton compiled in 1671 the Methodus Fluxionum at Serierum Infinitarum. In this book, Newton's strict empiricism shaped and defined his Fluxional Calculus. He exploited instantaneous motion and infinitesimals informally. He used math as a methodological tool to explain ...

• Word Count: 6149
• Approx Pages: 25
• Grade Level: Undergraduate

... examining their reliance on reasoning and imagination. Rigorous proof in mathematics is often derived from deductive and inductive reasoning. Deductive reasoning is the premise to achieve complete certainty: it is defined as "reasoning from general to particular" (Lagemaat 121). When applied to a system of numbers, real numbers can be narrowed down to different factors: irrational, rational, and whole numbers ... a completely new equation x³+y³=z³ based on his previous knowledge of Pythagorean theory and attempt to solve it (11.01.00). To elaborate, Euclid imagined a perfect pentagon...

• Word Count: 1304
• Approx Pages: 5
• Has Bibliography
• Grade Level: Undergraduate