Skip to main content

Important Mathematical Constants!

Important Mathematical Constants

Mathematical constants are those numbers that are special and interesting because they come up in the various fields of mathematics like geometry, calculus etc. These mathematical constants are usually named after the person who discovered it and they are represented by a symbol that is usually picked up from the Greek alphabet. Mathematical constants are by definition very important. In this article we will take a look at certain mathematical constants that are more commonplace than others.

1.     π (pi) or Archimedes constant (~3.14159):

 

π is defined as the ratio of the circumference of a circle to its diameter. This is probably the most popular mathematical constant. So π is the circumference of the circle whose diameter is 1 unit. You might have seen it popping up when calculating the area of a circle (πr2) or the circumference of a circle (2πr). It has many uses throughout mathematics from calculating the area of certain shapes to the Gaussian integral in complex analysis. π is irrational and is represented by the small letter π in the Greek alphabet.

2.     e or Euler’s constant (~2.71828):

 

e is also called the exponential growth constant. It is a very interesting number that shows very interesting properties. e is used in calculus. It is a very amazing number in general. The value of e can actually be calculated with compound interest. Imagine you have one rupee in the bank. The bank gives a compound interest of 100% per annum. So at the end of the year you will have 2 rupees. Imagine the bank, instead of giving you 100% per annum, gave 50% per six months. This is not equal to the above value. Therefore the final amount will be equal to 2.25 rupees (do the math). The value received has increased even though the principal is same. Imagine that for 33% per 4 months. The final value would be 2.36 rupees. Therefore it keeps on increasing. Then imagine how much you could get from 1/infinity % per 12/infinity months. You don’t have to. That number is e.

 

The formula is as follows:



e is also used in many other mathematical fields. It is used in Bernoulli trials, derangements, asymptotics, standard normal distribution and calculus.

 

If a graph is made with y=ex, it will show some unique properties too. At any point on the curved line formed on the graph, the y value of the point and the area under it are equal.

 

3.     i or the imaginary number (-10.5):

 

i is a very interesting variable. It’s value is the square root of -1. It falls into the category of imaginary numbers, in contrast to real numbers. Being a quadratic equation with a multiple root, i is not calculable. But other relations for i can be seen.

 

i2 = -1

i3 = i2i = (-1)i = -i

i4 = (-1)2 = 1

i5 = i3i2 = (-i)(-1) = i

 



It follows a certain pattern. The pattern is (-1, -i, 1, i). This is only applicable if we start with i4n+2. This leads to the conclusion that in = in mod 4 . ‘Mod’ refers to the modulus function.

 

 

 4.     √2 or “root 2” or Pythagorean constant (~1.414213):

√2 is a very well known mathematical constant. It is the ratio between the diagonal and side of a square. √2 is calculated by square rooting 2. It is based around the Pythagoras’ Theorem.

 

Let us assume x represents length of one side of a square. Let y assume the length of the side adjacent to it. x = y. Let z represent length of diagonal. x2 +  y2 = z2. This simplifies into 2x2 = z2. Therefore z = √2x. So the ratio z : x becomes √2x : x, which leaves you with √2.

Therefore √2 can be very easily proved geometrically. It is also a number whose infinite tetrate is equal to its square. This means:

√2 raised to the power to √2 raised to the power of √2 raised to the po……. infinitely = 2 or √22.


To be continued in part two…
This article is writen by Aman Thukral of Amity International School Noida. 




You may also like:

High School Pedia- www.highschoolpedia.com
Labels:

Comments

  1. tareekfabris4 March 2022 at 09:16

    Betway launches sports betting in India - KTHR
    Betway is India's 서산 출장마사지 leading online 광주 출장샵 sports betting and 시흥 출장샵 gambling operator. The 제주 출장마사지 online sports betting operator has taken steps to  Rating: 5 대전광역 출장마사지 · ‎Review by JKM Hub

    ReplyDelete
  2. Anonymous5 April 2022 at 20:57

    Bet365 Casino & Promos 2021 - JTM Hub
    Full goyangfc.com list of Bet365 Casino & Promos · Up to £100 in Bet Credits for new customers at bet365. Min deposit £5. https://vannienailor4166blog.blogspot.com/ Bet Credits available for https://septcasino.com/review/merit-casino/ use upon settlement of bets to www.jtmhub.com value of

    ReplyDelete

Post a Comment

Popular Posts

Animal and Plant Cells

 Cells Cells are the basic functional, biological and structural unit of life. The word cell is a Latin word meaning ‘small room’. Cells are also known as building blocks of life.  The branch of science that deals with the form, structure, and composition of a cell is known as Cytology. All organisms around us are made up of cells. Bacteria, ameba, paramecium, algae, fungi, plants and animals are made up of cells.  Cells together form tissues. And tissue together makes an organ. History Of Cell The cell was discovered by Robert Hooke in 1665. He assembled a simple microscope and observed a very thin slice of cork under his primitive microscope. The cork was obtained from the outer covering of a tree called bark. Robert Hooke observed many little-partitioned boxes or compartments in the cork slice. These boxes appeared like a honey-comb. He termed these boxes as the cell. He also noticed that one box was separated from another by a wa...
23 comments
Read more

Levitation 2

LEVITATION II To be completely honest I was going to start this with a pun. I did think of one but it doesn’t float… I am sorry I just had to. Anyway, this is the second part to the article on super cool ways of making things levitate. Go check the first part out if you haven’t already. Actually, the first part may have become repulsive with all the magnets and stuff, but I promise this will be more attractive. Get it? No? I’ll stop now. I am just going to jump straight into it. 1.    Electrostatic Levitation I know you are probably sick and tired of magnets but they are the best way you know… This method is somewhat similar. You remember that cool science experiment you did with two straws attracting or repulsing each other based on their charge? So basically using the same principle we can make a charged object levitate. But before you try it, let me tell you it won’t be easy. Even impossible according to our Mr. Earnshaw. He even made a law (th...
4 comments
Read more

High School Pedia

It is an initiative by some students to spread the light of knowledge to everyone and everywhere. It was started in the year 2015 and has grown rapidly in the past few months. By the means of this website, we try to provide information on every topic that we can reach up to. You can find different articles on this website. All these articles are written in simple language so that everyone can understand it and learn from it. We at High School Pedia believe in creative learning and this is the reason why we add our own edited graphical representations in every article. Once a very learned man said, “Knowledge increases by not keeping it to yourself but by sharing it with others”. And we follow the same motto “Share to Learn”. The team of High School Pedia tries its best to provide you with the best and original content. Unlike many other websites, High School Pedia is famous for its original and inspiring content.
2 comments
Read more

GLOBAL Telecommunications (texts topology) EXPLAINED!

messaging and texting is becoming a very easier and easier process nowadays as our typing speed has increased and delivering time is decreased.Speed entirely depends on us but ever wonder what actually happens to your typed message after you press a sent button. If not then its wonderful because today in this one we are going to discuss abut the same. So lets get started. TELECOM OF TEXTS  Actually the full path of your message after you have of-course typed it and press the send button can be simplified into a simple process which include many entities with different tasks to perform. well yes! that`s pretty much of the process and for the time being we would be continuing TO understand the same. HP 1 - Is considered to be the sender of the message or text. HP 2 -Is considered to be the receiver of the message or text of HP 1. BASE TRANSCEIVER STATION or BTS - {also known as cell sites}They are towers which are currently present in hundreds in your city o...
3 comments
Read more

Working of a Car Engine

CAR ENGINE Hi, guys!  You must have thought that how a car engine works. So this is the right article for you. Describing It An engine is described by its structure and the number of the piston it is made up of. For eg: the following engine has v6 90 °. (This is just a part of engine and not the whole)    
7 comments
Read more

Stains And Dyes

STAINS AND DYES Stains and dyes are used to great lengths in microbiology to highlight certain parts or organelles of cells when put under the microscope. They can also be used to classify the various parts of the cells and different cell groups in a tissue. Stains can be used on their own as well as mixed with other stains and dyes. In fact, the process of using multiple stains to highlight important parts of an already stained cell is called counterstaining. You may have used safranine while preparing a temporary mount of leaf peel to observe stomata. That is an example of a stain. When it comes to the process of applying stains, there are broadly two different classifications: IN VIVO staining and IN VITRO staining. As the name suggests, IN VIVO staining is practised on live tissue. It helps us observe the chemical reactions taking place within a living cell. Stains are used here to highlight the chemicals and chemical reactions taking place. IN VITRO staining is pract...
Post a Comment
Read more

Important Mathematical Constants!

Important Mathematical Constants Mathematical constants are those numbers that are special and interesting because they come up in the various fields of mathematics like geometry, calculus etc. These mathematical constants are usually named after the person who discovered it and they are represented by a symbol that is usually picked up from the Greek alphabet. Mathematical constants are by definition very important. In this article we will take a look at certain mathematical constants that are more commonplace than others. 1.       π (pi) or Archimedes constant (~3.14159):   π is defined as the ratio of the circumference of a circle to its diameter. This is probably the most popular mathematical constant. So π is the circumference of the circle whose diameter is 1 unit. You might have seen it popping up when calculating the area of a circle (πr 2 ) or the circumference of a circle (2πr). It has many uses throughout mathematics from calcula...
4 comments
Read more