Q: Why is phi an irrational number?

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They are all points on the [Real] number line.However, different irrational numbers: pi, sqrt(2), e, phi etc have different geometric applications.

The value of phi is NOT 3.14. The value of phi, the Golden ratio, is [sqrt(5)+1]/2 which is approximately 1.62. It is an irrational number and so it has an infinitely long, non-recurring decimal representation.

Pi is infinite & digits never end. 3.14159 are amongst the first. * * * * * The answer given above is for pi. The question was about phi - which is usually used to indicate the Golden Ratio! Like pi, phi is irrational - but unlike pi, is not transcendental. Phi = [1 + sqrt(5)]/2 = 1.61803 approx.

The golden number? Phi = 1.61803398872...

An irrational number.

Related questions

It depends on what phi is being used for. Generally, phi is used to represent the Golden Ratio, [1+ sqrt(5)]/2. In that case phi is an irrational number approximately equal to 1.6180

Yes. For example, if you multiply the square root of 2 (an irrational number) by itself, the answer is 2 (a rational number). The golden ratio (Phi, approx. 1.618) multiplied by (1/Phi) (both irrational numbers) equals 1 (rational). However, this is not necessarily true for all irrational numbers.

-4.9 is a rational number. If a number is irrational, then it can not be expressed as a finite number of digits. A few examples of irrational numbers are: pi, the square root of any integer which is not square and the golden ratio (phi).

They are all points on the [Real] number line.However, different irrational numbers: pi, sqrt(2), e, phi etc have different geometric applications.

It can be a real number which is not a rational number. That is, an irrational number such as sqrt(2), or cuberoot(5), or pi, or e, or phi. Or it can be a number that is not even a real number, such as a complex number or a quaternion.

Rational. An irrational number is something that cannot be written as a fraction of integers and since they can't be written this way they will not end. Irrational numbers are numbers like pi, phi, e (Euler's number) and a lot of square roots.

The value of phi is NOT 3.14. The value of phi, the Golden ratio, is [sqrt(5)+1]/2 which is approximately 1.62. It is an irrational number and so it has an infinitely long, non-recurring decimal representation.

Yes. It is equal to (1 + sqrt5) / 2 = ~1.618 which, though irrational, is a purely real number; i.e. it has no imaginary component.

Numbers like these ( pi, phi, imaginary number i ), are called IRRATIONAL NUMBERS.

Pi is infinite & digits never end. 3.14159 are amongst the first. * * * * * The answer given above is for pi. The question was about phi - which is usually used to indicate the Golden Ratio! Like pi, phi is irrational - but unlike pi, is not transcendental. Phi = [1 + sqrt(5)]/2 = 1.61803 approx.

The golden number? Phi = 1.61803398872...

It depends on the level of mathematics. At the basic level, it usually is, but you can get surds in which the numerator (top) is an irrational number.The Golden ratio, phi = [1 + sqrt(5)]/2. The top is 1 + sqrt(5), an irrational term.The measure of a right angle (in radians) is pi/2. Again, an irrational number, on top.