What is pi? How do we use it in life?

Answer 1

See below.

What is #pi#?
The simplest definition of #pi# is the ratio of the circumference of any circle to its diameter. It can be proved that #pi# is a constant.
So, for a circle of radius #r#, #pi = C/(2r)# where #C# is the circumference of the circle.
It can be proved that #pi# is an irrational number, that is it cannot be expressed as a fraction. [Strictly, it cannot be expressed by any #p/q: {p,q} in ZZ, q!=0#]
Since #pi# is irrational it can never be exactly evaluated by any finite decimal. Thus, #pi# can only ever be approximated by a value of arbitrarily many decimal places.
Whilst there have been many approximation formulae discovered, an efficient approximation of #pi# was found by Leonard Euler in the 18th century to be:
#pi^2/6 = sum_(i=1)^oo 1/i^2 ->pi approx 3.1415926535897932384626433...#
[NB: It can also be proved that #pi# is a transcendental number. That is it cannot be the root of any polynomial equation with real coefficients.]
How is #pi# used in real life?
The practical uses of #pi# are too numerous to set out here. I'll list a few basic examples below.
(i) As can be seen from the definition above, using #pi# we can find the circumference of a circle of radius #r# which is #2pir#
(ii) The area of a circle of radius #r# is #pir^2#
(iii) The volume of a sphere of radius #r# is #4/3pir^3#
There are a vast number of instances involving #pi# in the physical world as well as many other applications in pure mathematics.
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

Pi (π) is a mathematical constant representing the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. It is an irrational number, meaning it cannot be expressed as a simple fraction, and its decimal representation goes on infinitely without repeating.

In life, pi is used in various fields and applications:

  1. Geometry: Pi is fundamental in geometry for calculating the circumference, diameter, area, and volume of circles, spheres, cylinders, and cones.

  2. Engineering: Engineers use pi extensively in designing structures, machinery, and systems involving circular or cylindrical components, such as bridges, gears, and pipelines.

  3. Physics: Pi appears in formulas related to wave phenomena, oscillations, and harmonic motion, as well as in equations describing the behavior of electrons in quantum mechanics.

  4. Architecture: Architects use pi to design and construct buildings with circular or curved features, such as domes, arches, and columns.

  5. Technology: Pi is utilized in various technological applications, including computer graphics, image processing, and digital signal processing.

  6. Statistics: Pi is occasionally used in statistical analysis, particularly in fields like physics and engineering where it appears in probability distributions and statistical models.

Overall, pi is a fundamental constant that permeates many aspects of mathematics, science, engineering, and technology, playing a crucial role in understanding and solving real-world problems and phenomena.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7