Nature and History of Mathematics

These flashcards cover key concepts in the nature and history of mathematics, their definitions, and important figures.

Nature of Mathematics

Mathematics reveals the simplicities of nature and helps generalize from simple examples to complex real-world situations.

Egyptians

Developed a positional number system, base 10, and foundational arithmetic operations around 3000 BC.

Babylonians

They utilized a sexagesimal positional number system and solved equations with multiple unknowns between 1700 - 300 BC.

Pythagorean Theorem

States that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

Planetary Motion

Discovered by Johannes Kepler, stating that planets move in elliptical orbits around the sun.

Cartesian Plane

Developed by René Descartes, it bridges algebra and geometry, resulting in the Cartesian coordinate system.

Pascal's Triangle

A triangular array of binomial coefficients discovered by Blaise Pascal, key in probability theory.

Calculus

Established by Isaac Newton and Gottfried Leibniz, it includes the study of rates of change and areas under curves.

Fibonacci Sequence

A sequence where each number is the sum of the two preceding ones, important in various natural patterns.

Golden Ratio

A mathematical ratio of approximately 1.6180339887, often appears in nature, art, and architecture.

Polygons

Two-dimensional shapes with straight sides, classified as regular (equal sides) or irregular.

Geometric Transformations

Changes in size, orientation, or position of geometric shapes, including translation, rotation, reflection, and dilation.

Mathematical Language

A precise, concise language used to express complex ideas through symbols and terms.

Sets in Mathematics

A well-defined collection of distinct objects or ideas, often represented with braces {}.

Finite Set

A set where all elements can be listed, such as the set of countries in the world.

Infinite Set

A set with elements that cannot be fully listed, such as counting numbers greater than 10.