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College Algebra: Help and Review27 chapters | 230 lessons | 1 flashcard set

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Blaise Pascal contributed much to mathematics in his short 39 years. In this lesson, you will learn that he laid the foundation for probability. To help his father, Blaise even designed a calculator to make tax calculations easier.

**Blaise Pascal** lived in 17th-century France and made several contributions to the fields of mathematics, physics, and philosophy. He is known for laying the foundation for today's probability theory, for his work in barometric pressure, and for his theological writings.

Blaise Pascal made contributions to mathematics, physics, and philosophy. In mathematics, you might recognize his name in **Pascal's triangle**. The numbers that form Pascal's triangle are binomial coefficients. Each number is the sum of the two numbers above it. The tip of the triangle and the sides are all ones. The numbers forming the body of the triangle are the addition of the two immediately above. For example, the middle number in the third row is the addition of the two numbers from the second row. Pascal presented this information in written form in 1653.

A year later, Pascal laid the foundation for **probability theory**. He was inspired by his desire to help a friend who had some questions about gambling. He realized that events don't happen randomly, but actually depend on what happened just before the event. In other words, if you had a box of blue and red balls, and you had already taken a blue ball out, the probability of taking a red ball out now will have changed.

In 1646, Blaise Pascal experimented with atmospheric pressure and discovered that vacuums exist in the real world. He also found that atmospheric pressure can be measured using real weights. After a conversion experience, Blaise Pascal fully converted to Jansenism and wrote the *Provincial Letters* in which he defended Jansenism and its leading philosopher against the Jesuits.

In the year 1642, at just 18 years old, Pascal invented a calculator to help out his father. This calculator was called the Pascaline and had a wheel with eight movable parts for dialing. Each part corresponded to a particular digit in a number. For example, the number 368 would be dialed in three parts with a three, six, and eight, respectively for the hundreds, tens, and ones position. The Pascaline could add, subtract, multiply, and even divide. This was an early form of the now standard digital calculator.

Also in the 1640s, while tinkering with barometric pressure, Blaise Pascal invented the syringe and the hydraulic press. Today, we see syringes in health facilities everywhere, and hydraulic presses are used in auto shops to lift up cars and in many other applications. Another invention of Pascal's was the roulette machine in 1655. This invention was actually an accident that resulted when Pascal tried to invent a perpetual motion machine that would produce energy.

Blaise Pascal only lived for 39 years, but they were 39 years full of discoveries, learning, and creativity. Born on June 19, 1623 in France, Blaise Pascal lost his mother only three years after in 1626. He died himself on August 19, 1662 in Paris.

Surprisingly, Pascal's father prevented his young son from learning geometry during his early years. Because geometry and mathematics were off-limits, young Pascal felt an even stronger urge to learn the subjects. So, when he was just 12 years old, he started learning geometry on his own. He even figured out that the sum of the angles in a triangle add up to 180 degrees on his own.

Because his father saw how smart he was, Pascal was finally allowed to study mathematics. He even went to meetings held at the Paris mathematics academy. It was at this academy that Pascal presented his first theorems when he was only 16 years old.

Let's review. **Blaise Pascal**, in his short 39 years of life, made many contributions and inventions in several fields. He is well known in both the mathematics and physics fields. In mathematics, he is known for contributing Pascal's triangle and probability theory. He also invented an early digital calculator and a roulette machine.

In the field of physics, Blaise contributed to the study of atmospheric pressure by discovering that vacuums are real and exist in the real world. From his study of atmospheric pressure, he invented the syringe and hydraulic press. While he is known for his contributions and inventions in mathematics and physics, Pascal's father actually prevented him from studying mathematics as a child. But, Pascal was curious and cut a path of his own, becoming a child prodigy.

Following this lesson, you'll have the ability to:

- Summarize Blaise Pascal's life and the importance of his work
- Recall examples of Pascal's important contributions to mathematics, physics, and philosophy
- Identify four of Pascal's inventions

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College Algebra: Help and Review27 chapters | 230 lessons | 1 flashcard set

- Go to Fractions

- Go to Factoring

- What Is a Factorial? 5:24
- Factorial Practice Problems 6:04
- What is the Binomial Theorem? 9:14
- Binomial Theorem Practice Problems 7:08
- Blaise Pascal: Contributions, Inventions & Facts 5:10
- Bayes' Theorem Practice Problems 11:17
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