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This lecture discusses the 16th century philosopher, theologian, and mathematician, Blaise Pascal, and focuses on his work, the Pensees. 

Specifically it discusses the passage in which he writes: "C’est une sphère infinie dont le centre est partout, la circonférence nulle part" (71, in the Léon Brunschvicg edition). As it turns out, this expression has a history, and Pascal also adds to the concepts involved in a few other passages.


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Pascal Pensees - The Infinite Sphere, Its Circumference, And Its Center - Sadler's Lectures

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Lesson 1 Homework Practice Circumference

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Lesson 1 Homework Practice: Circumference

In this lesson, you will learn how to calculate the circumference of a circle, which is the distance around the edge of the circle. You will also learn how to use the formulas for circumference in different situations. You will need a calculator and a ruler for this lesson.

What is the circumference of a circle?

The circumference of a circle is the linear distance of a circle's edge. It is similar to the perimeter of a polygon, but the term perimeter is used only for shapes with straight sides. The circumference of a circle depends on its diameter or radius, which are measurements of the circle's size.

What are the formulas for circumference?

There are two main formulas for finding the circumference of a circle, depending on whether you know the diameter or the radius of the circle. The diameter is the longest distance across the circle, passing through the center. The radius is half of the diameter, or the distance from the center to any point on the edge. The formulas are:


C = πd, where C is the circumference and d is the diameter.
C = 2πr, where C is the circumference and r is the radius.


In both formulas, π (pi) is a constant that is approximately equal to 3.14 or 22/7. It is an irrational number, which means it cannot be written as a fraction or a decimal with a finite number of digits. You can use your calculator to find its numerical value.

How to find the circumference of a circle using the diameter?

If you know the diameter of a circle, you can use the formula C = πd to find its circumference. Here are the steps:


Measure or find out the diameter of the circle.
Plug the value of the diameter into the formula and multiply it by π.
Round your answer to an appropriate level of accuracy.


For example, suppose you have a circular plate with a diameter of 10 inches. To find its circumference, you can follow these steps:


The diameter of the plate is 10 inches.
C = πd = π x 10 = 31.4 inches.
Rounding to one decimal place, the circumference is 31.4 inches.


How to find the circumference of a circle using the radius?

If you know the radius of a circle, you can use the formula C = 2πr to find its circumference. Here are the steps:


Measure or find out the radius of the circle.
Plug the value of the radius into the formula and multiply it by 2π.
Round your answer to an appropriate level of accuracy.


For example, suppose you have a circular cookie with a radius of 3 inches. To find its circumference, you can follow these steps:


The radius of the cookie is 3 inches.
C = 2πr = 2π x 3 = 18.8 inches.
Rounding to one decimal place, the circumference is 18.8 inches.

How to solve word problems involving circumference?

Sometimes, you may encounter word problems that require you to find the circumference of a circle or use the circumference to find other information. To solve these problems, you need to read the problem carefully, identify the given information and the unknown quantity, and use the appropriate formula for circumference. Here are some examples of word problems involving circumference:

Example 1

A circular pond has a diameter of 12 meters. What is the length of the fence that surrounds the pond?

Solution:

In this problem, we are given the diameter of the pond and we need to find the length of the fence. The length of the fence is equal to the circumference of the pond. We can use the formula C = πd to find the circumference.


The diameter of the pond is 12 meters.
C = πd = π x 12 = 37.7 meters (rounded to one decimal place).
The length of the fence is 37.7 meters.


Example 2

A bicycle wheel has a radius of 35 centimeters. How many times does the wheel turn when the bicycle travels 1 kilometer?

Solution:

In this problem, we are given the radius of the wheel and we need to find the number of times it turns. The number of times the wheel turns is equal to th

Lesson 1 Homework Practice Circumference

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