Blaise Pascal: A Unit Study

Blaise Pascal: A Unit Study
Blaise Pascal: A Unit Study


Blaise Pascal was a French Renaissance scientist, mathematician, inventor, and theologian who was born on June 19, 1623.

Pascal’s Beginnings

Pascal’s mother died when he was three years old. Pascal’s father Étienne was a wealthy government official. He studied law but was also a talented mathematician and musician. After his wife died he decided to educate his children at home. They were all considered to have exceptional intellectual ability. Blaise Pascal never received a formal education.

Pascal and Mathematics

When a teenager, Pascal began studying Euclid’s geometry. His natural talent for the subject led to his developing Pascal’s Theorem at the age of 16, which states that, given a hexagon inscribed in a conic section, the three pairs of the continuations of opposite sides meet on a straight line, called the Pascal Line.

Pascal also developed the first calculating machine in 1642. As a tax collector, Pascal’s father had to add many large columns of numbers. The calculating machine used gears with ten teeth each. Ten turns of one gear advanced the next gear by one. Known for developing his ideas into practice, he enlisted the help of a craftsman who helped him construct the machine.

Interestingly, it was his interest in calculating probabilities that led to Pascal’s Triangle, thought by many to be a precursor to calculus developed by Isaac Newton and Gottfired von Leigniz nearly 30 years later. In Pascal’s Triangle each number is the sum of the two numbers above it.

Pascal Triangle

There are many patterns that can be found in the triangle, one of which is binomial expansion.

Pascal and Science

Torricelli created a mercury barometer in 1644. Deciding to disprove the axiom “nature abhors a vacuum,” Pascal decided to test the axiom by seeing what would happen if the mercury was forced up the barometer tube by air pressure. In the process, Pascal developed his Law of Fluid Pressure, which states that a force applied to a confined fluid will be distributed throughout the fluid equally independent of the container.

Pascal stridently exercised the scientific method, maintaining that the evidence of experimental data carries more weight than traditional views held by even the most venerated. Through this exercise, he proved that air pressure is lower the higher you go up a mountain.

Pascal’s Principle: The pressure on any area depends on the height of the column of liquid upon or against the area.

In 1971 the International System of Units adopted the name pascal (Pa) for Newtons per meter squared — a unit that is used to measure pressure.

Pascal and Theology

As a young man Pascal was very eager to define truth. At age 31 Pascal became a Jansenist. Jansenists believed that only the chosen were capable of receiving God’s grace. They also believed that man did not have the ability to choose good or evil. He spent the remainder of his life writing Apology for the Christian Religion, which he never finished. Most of the work was merely fragments. However, after his death these fragments were collected and published in 1670 under the name Pensees, meaning thoughts. The focus was on man’s insignificance and his need for God.

Pascal’s Death

Pascal died August 19, 1692. He had been in ill health nearly his entire life. The translation of his epitaph reads as follows:

Illustrious for his great knowledge which was recognized by the scholars of all Europe; more illustrious still for the great probity which he exercised in the offices and employments with which he was honored; but much more illustrious for his exemplary piety. He tasted good and bad fortune, that he might be known in every thing for what he was. He was seen temperate in prosperity and patient in adversity. He sought the aid of God in misfortune, and rendered him thanks in happiness. His heart was devoted to his God, his king, his family, and his friends. He had respect for the great and love for the small; it pleased God to crown all the graces of nature that he had bestowed on him with a divine grace which made his great love for God the foundation, the stay, and the consummation of all his other virtues.

Thou, who seest in this epitome the only thing that remains to us of so beautiful a life, admire the fragility of all present things, weep the loss that we have suffered; render thanks to God for having left for a time to earth the enjoyment of such a treasure; and pray his goodness to crown with his eternal glory him whom he crowned here below with more graces and virtues than the limits of an epitaph permit us to relate.

His grief-stricken children have placed this epitaph on this spot, which they have composed from the fulness of their hearts, in order to render homage to the truth and not to appear ingrates in the sight of God.

Further Investigation

Blaise Pascal
Biography for students from the Lemelson MIT Program.

The Barometer Experiments of Blaise Pascal
Described in detail.

Activities

Coloring Multiples in Pascal’s Triangle
Interactive.

Pascal’s Law Science Experiment
Simple experiment to demonstrate.

Pascal’s Theorem
Interactive that allows you to experiment to understand the theorem.

Books

Pascal’s Pensees by Blaise Pascal
In the public domain.

Christianity for Modern Pagans

Christianity for Modern Pagans: Pascal’s Pensees Edited, Outlined, and Explained by Peter Kreeft
Guide for older students.

Lesson Plans & Unit Studies

Pascal’s Triangle
Lesson at MathIsFun.com.

Pascal’s Triangle
Lesson plan from YouCubed at Stanford for younger students.

Pascal’s Triangle
Free lesson and worksheets at TeachersPayTeachers.com for upper grade school students.

Pascal’s Triangle
Free lesson and worksheets at TeachersPayTeachers.com for high school students.

What is Pressure
Lesson at Khan Academy.

Printables & Notebooking Pages

Pascal’s Triangle Worksheet
Great for wrapping up!

Blaise Pascal Notebooking Pages
Simple pages for copywork, narrations, or wrapping up.