In thirteen books he collected The Elements of geometry, starting from the most basic concepts, "a point is that which has no part- and "a line is breadthless length-. After stating that "the extremities of a line are points- and postulating that it is possible "to draw a straight line from any point to any point-, he opened the doors to a realm of perfect forms, or figures, that can only exist in our minds. ... Focusing our mind on the metaphysical plane where the triangle exists and by following Euclid's reasoning we find that we too can have access to that realm where we'll see tr...

• Word Count: 1043
• Approx Pages: 4
• Grade Level: Undergraduate

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 to represent sets, subsets and set operations; solves problems involving sets; describes and illustrates the absolute value of a number on a number line as the distance of the number from 0; performs fundamental operations on integers; addition, subtraction, multiplication, division; states and illustrates the different properties of the operations ...

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

Richard Dedekind: An Algebraic Foundation for Calculus In 1858, while giving lectures on differential calculus, mathematician Richard Dedekind noted the lack of a truly scientific foundation of the arithmetic with which he taught his class. Realizing this flaw, Dedekind was motivated to improve ...

• Word Count: 2467
• Approx Pages: 10
• Has Bibliography
• Grade Level: Undergraduate

Thereafter, calculus was actively used to solve the major scientific dilemmas of the time, such as:- Calculating the slope of the tangent line to a curve at any point along its length Determining the velocity and acceleration of an object given a function describing its position, and designing such a position function given the object's velocity or acceleration Calculating arc lengths and the volume and surface area of solids Calculating the relative and absolute extrema of objects, especially projectiles. -----------------------------------...

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