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## Is pi over 2 rational or irrational?

It is an irrational number. A number is rational if it can be expressed as a quotient of 2 integer numbers. Number π2 cannot be expressed as a quotient of integers, so it is an irrational number.

## Is 2 pi squared rational?

Theorem. Pi squared (π2) is irrational.

**Is 2 pi A irrational?**

2. π is an irrational number because it has a non-terminating and non-repeating decimal expansion.

**Why is π 2 irrational?**

π is transcendental, meaning that it is not the root of any polynomial equation with integer coefficients. Hence π2 is transcendental and irrational too. Since π is not the root of any polynomial with integer coefficients, let alone a quadratic, this is not possible.

### Is pi irrational?

Pi is an irrational number—you can’t write it down as a non-infinite decimal. This means you need an approximate value for Pi.

### Is pi 3 rational or irrational?

1 Answer. 3π is irrational.

**Is pi pi irrational?**

No matter how big your circle, the ratio of circumference to diameter is the value of Pi. Pi is an irrational number—you can’t write it down as a non-infinite decimal. This means you need an approximate value for Pi.

**Who proved pi 2 irrational?**

Ferdinand von Lindemann

In 1882, Ferdinand von Lindemann proved that π is not just irrational, but transcendental as well.

#### Is pi irrational or rational?

irrational number

Pi is an irrational number, which means that it is a real number that cannot be expressed by a simple fraction. That’s because pi is what mathematicians call an “infinite decimal” — after the decimal point, the digits go on forever and ever.

#### Is pi rational or irrational?

No matter how big your circle, the ratio of circumference to diameter is the value of Pi. Pi is an irrational number—you can’t write it down as a non-infinite decimal. This means you need an approximate value for Pi.

**Is pi in a fraction irrational?**

Pi is an irrational number, which means that it is a real number that cannot be expressed by a simple fraction. That’s because pi is what mathematicians call an “infinite decimal” — after the decimal point, the digits go on forever and ever.

**Who proved pi is irrational?**

mathematician Ivan Niven

Canadian mathematician Ivan Niven has provided us with a proof that π is irrational. This proof requires knowledge of only the most elementary calculus. The difficult part is following the trail of the argument. His paper, enticingly titled A Simple Proof That π Is Irrational is just one page long.

## Is pi/pi rational or irrational?

However, Pi/Pi is equivalent to 1, which is certainly rational. Is it most accurate to say that Pi/Pi is irrational (by definition), but that it is equivalent to a rational number? That seems problematic, since it implies a number can be both rational and irrational at the same time.

## Is π/2 an irrational number?

Since all rational numbers are Algebraic, 2 is algebraic, and the product of algebraic numbers is algebraic, this implies that π is also algebraic. But it is well known [ 1] that π is a Transcendental number. This contradiction implies that π / 2 is irrational.

**What are some examples of rational and irrational numbers?**

Examples of rational numbers are ½, ¾, 7/4, 1/100, etc. Examples of irrational numbers are √2, √3, pi (π), etc. π is an irrational number which has a value of 22/7 or 3.142…and is a never-ending and non-repeating number.

**Is Pi an algebraic number?**

It is irrational. If it were rational, then π = 2 q where q is rational. Since all rational numbers are Algebraic, 2 is algebraic, and the product of algebraic numbers is algebraic, this implies that π is also algebraic.