Pi is transcendental. What does this mean, in mathematics?

It cannot be expressed as an integer, or as a root or quotient of integers

It is equal to the ratio of two integers

It was Ralph Waldo Emerson’s favorite number.

What is the earliest known reference to pi in history?

An Egyptian papyrus scroll, written approx. 1650 BC by Ahmes the Scribe

The Rosetta Stone, approx. 200 BC

Euclid’s Elements, written in the 3rd century BC

People tried for centuries to “square the circle”. What were they trying to do?

Use a straightedge and compass to construct a square exactly equal in area to a given circle

Construct a square that perfectly circumscribes (surrounds) a given circle

Determine the value of pi squared

Alter a recipe intended for a round pan so that it would fit exactly into a square pan

Are pi’s digits periodic? In other words, do the digits ever repeat themselves in any pattern?

No. Every periodic number is rational, but pi is irrational

Yes. The digits repeat themselves every 6,000,000 decimal places

Yes. Every infinitely long number repeats itself

Perhaps. Not enough digits of pi have been calculated to know yet

Pi is an irrational number. What does that really mean?

it is a real number, but can’t be expressed as a ratio of two integers

Its digits cannot be rationed out evenly

Nobody with sound judgement has anything to do with it

What is the “formal” definition of pi?

the ratio of a circle’s circumference to its diameter

the surface area of a sphere of diameter 22/7

Imagine if you wrapped a rope tightly around the earth at the equator. How much longer would you have to make the rope if you wanted it to be exactly one foot above the surface all the way around?

2 ∏ r feet, where r is the radius of the earth

Value of Pi in Maths - Definition, Symbol, and Examples

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Updated: Jan 17, 2025

Lesson

What Is Pi (π)?

Pi (π) is a special number used in mathematics. It is the ratio of a circle's circumference (the distance around the circle) to its diameter (the distance across the circle). This ratio is the same for all circles, no matter their size.

Pi is an irrational number. This means its decimal form goes on forever without repeating.

What Is the Value of Pi in Maths?

The value of Pi is approximately 3.14159, but we often use 3.14 for simple calculations.
Here is Pi written out:
3.141592653589793238…

Example: Imagine you're calculating the circumference of a circle. The formula is:

Circumference = π × Diameter

If the diameter of your circle is 5 cm, you can use Pi as 3.14 for simplicity:

Circumference = 3.14 × 5 = 15.7 cm

If you use the more accurate value of Pi (3.14159):

Circumference = 3.14159 × 5 = 15.70795 cm

So, using the more accurate value of Pi gives a slightly more precise result.

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Integers Quiz Questions and answers

What Is Pi Used For?

Pi is used in formulas related to circles and curves. For example:

To find the area of a circle: Area = π × radius²
To find the circumference of a circle: Circumference = 2 × π × radius

How to Calculate the Value of Pi

Steps to Calculate Pi:

Measure the Circumference of a Circle:
- The circumference is the distance around the outer edge of the circle. Use a ruler or measuring tape to measure it.
Measure the Diameter of the Circle:
- The diameter is the distance from one side of the circle to the other, passing through the center. You can measure it with a ruler.
Use the Formula:
- The formula to calculate Pi is:

Pi = CircumferenceDiameter

Perform the Division:
- Divide the circumference by the diameter.
Result:
- The result will give you the value of Pi, which is approximately 3.14, but it can be more precise (e.g., 3.14159) based on how many decimal places you use.

Example 1:

If a circle's circumference is 31.4 cm and its diameter is 10 cm, we can calculate Pi by dividing the circumference by the diameter.

Pi = Circumference ÷ Diameter

Pi = 31.4 ÷ 10 = 3.14

So, the value of Pi is 3.14.

Example 2:

If a circle's circumference is 62.8 cm and its diameter is 20 cm, we calculate Pi by dividing the circumference by the diameter.

Pi = Circumference ÷ Diameter

Pi = 62.8 ÷ 20 = 3.14So, the value of Pi is again 3.14.

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How much do you know about Pi Quiz ?

Solved Example of Pi

Here are a few easy examples of Pi.

Example 1:

Imagine you're riding your bike around a circular track. The track's total distance (circumference) is 31.4 cm, and the width (diameter) is 10 cm.

Step 1: To figure out how much the track curves (π), use the formula:
π = Circumference ÷ Diameter

Step 2: Plug in the values:
π = 31.4 ÷ 10

Step 3: Do the math:
π = 3.14

So, the magic number for your bike's track is 3.14!

Example 2:

You're making a bracelet with a circular bead. The bead's circumference is 62.8 cm, and the diameter is 20 cm.

Step 1: Use the formula to find π:
π = Circumference ÷ Diameter

Step 2: Substitute the numbers:
π = 62.8 ÷ 20

Step 3: Divide:
π = 3.14

And guess what? The π for your bracelet is 3.14!

Example 3:

You're measuring the wheel of your toy car. The wheel's circumference is 15.7 cm, and the diameter is 5 cm.

Step 1: Use the π formula:
π = Circumference ÷ Diameter

Step 2: Plug in the values:
π = 15.7 ÷ 5

Step 3: Do the math:
π = 3.14

Your toy car's wheel also gives 3.14!

Example 4:

You're designing a frisbee, and its circumference is 125.6 cm with a diameter of 40 cm.

Step 1: Use the formula to find π:
π = Circumference ÷ Diameter

Step 2: Insert the numbers:
π = 125.6 ÷ 40

Step 3: Calculate:
π = 3.14

Now you know, your frisbee's π is 3.14!

Example 5:

Imagine you're tracing a tiny pie's edge. Its circumference is 9.42 cm, and the diameter is 3 cm.

Step 1: Use the formula to find π:
π = Circumference ÷ Diameter

Step 2: Plug in the numbers:
π = 9.42 ÷ 3

Step 3: Perform the division:
π = 3.14

Looks like your mini pie's π is also 3.14!

Pi Assessment

Calculate the area of a circle with a radius of 10 cm.

What is Pi?

Write the approximate value of Pi.

Find the circumference of a circle with a diameter of 8 cm.

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Aptitude and PI Test

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