French mathematician and philosopher Blaise Pascal was born in 1623.

Because of his father’s unusual ideas about education, Blaise Pascal was forbidden to study mathematics until he was 15 years old. His curiosity roused by the prohibition, Pascal began to study geometry secretly when he was 12. When his father discovered that Pascal had figured out by himself that the sum of the angles of a triangle is two right angles, he lifted his ban on math. Pascal’s father was also the driving force behind his invention of the first digital calculator, called the Pascaline, which he designed to help his father with his work as a tax collector. Pascal made a number of contributions to mathematics, including laying the groundwork, along with Fermat, for the study of probability. His name is associated with Pascal’s Triangle, a triangular arrangement of numbers that contains multiple patterns. Although the triangle existed long before Pascal, he is credited with having discovered all its patterns. Pascal’s law of pressure, a physical law concerning the equilibrium of water, also bears his name. Pascal performed experiments on atmospheric pressure as well, which essentially proved that vacuums exist. After a life-threatening accident in 1654, Pascal devoted his life to religion. He published numerous philosophical and theological works, including the Pensées, in which he offers his famous “wager” justifying the rationality of theistic belief.

Illuminations
Students examine Pascal’s triangle as part of an exploration of patterns in a variety of mathematical contexts in Patterns that Grow (3–5).

Learning about Number Relationships and Properties of Numbers Using Calculators and Hundred Boards: Patterns to 100 and Beyond (K–2) furnishes a visual way of highlighting and displaying various patterns and relationships among numbers.

In Counting Embedded Figures (9–12), students look for patterns within the given data.

Calculators have changed dramatically since Pascal’s original version. The lesson Line ‘Em Up (6–8) uses a graphing program for Texas Instruments graphing calculators to teach students to plot a point (given its coordinates) and to state the coordinates of a given point.

Science NetLinks
In Marble Mania (3–5), students begin to develop a basic understanding of probabilities. By flipping coins and pulling marbles out of a bag, students discover how probabilities are determined and how the outcome of an experiment can be affected by the number of times it is conducted.