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.     Ï€ (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:
Important mathematical constants
Sets, Relation and functions
Pareto's Principle
Zipf's Law
Clock And Calendar
Permutation and Combination
Multiplication(Vedic Maths)
Square Root(Vedic Maths)
Inverse Trigonometric functions
2-D & 3-D GEOMETRY
Human and Plants Cells
High School Pedia : www.highschoolpedia.com
Labels:

Comments

  1. fgfgf27 March 2022 at 13:09

    Address : 33 Chester Road West, Deeside, CH5 1SA

    Phone : 0203-858-0302

    Capital Services Group was created with one mission in mind: to provide tailored solutions designed to resolve all your servicing needs.Capital Service Group Our team of dedicated specialists are committed to providing the highest quality service every time. Rest assured that no matter the service your needs are in safe hands.

    ReplyDelete
  2. fgfgf28 March 2022 at 18:50

    Address : Room B8, 1/F, Block B, East Sun Industrial Building,16 Shing Yip St, Kwun Tong, Kowloon, Hong Kong

    Phone : +852 5448 6841

    skincare wholesale We first started just as a lattice shop in Hong Kong. If you don't know what that is, it simply refers to a small area divided from the shelf , and we owned one of them.

    We were small, but we were serious about finding reliable suppliers.

    It wasn't plain sailing. Spammers, overpriced or expired products, inauthentic items, orders that took forever to ship, irresponsible outsourcing partners, dubious companies... you name it, we have experienced them all.

    So we thought, why don't we build our own trustworthy one-stop beauty platform? Not only for our retail customers but also those businessmen who are serious about finding reliable wholesalers as we did.

    And here we are, Carsha.

    Our Mission
    We aspire to build an all-in-one beauty marketplace for our retail customers by gathering together a diverse range of products, from global-leading brands to indie beauty brands. Towards our B2B customers, we aim to become their most transparent, accessible, best-price and supportive beauty wholesaler.

    Our Vision
    Our goal is to provide our customers with a personalized, informative, and supportive shopping and purchasing experience. We also empower people, including our employees and companies of all sizes, to achieve beauty, confidence, and success. Finally, we hope that Carsha can evolve alongside the rest of the world.

    Our Promise
    We guarantee that we treat you just like how we treat ourselves - that means that all our products will be 100% authentic. On top of that, our collections will expand from day to day to assure you to be able to find the most suitable cosmetics, skincare products, or fragrances for you and your business. Last but not least, our customer service will remain the best all the time.

    Our Impact
    Over 1500 customers were able to save money thanks to our beauty deals. Over 100 businesses benefited from our products and were inspired by our one-of-a-kind and personalized business strategies. More than 20 employees benefited from our environment and learned from us. In the future, we hope to give back to society by focusing on orphanages, homelessness, and mental illness.

    ReplyDelete
  3. fgfgf4 April 2022 at 21:33

    Address : Alfred-Escher Strasse 66, 8002 Zurich

    Phone : +41 44 280 29 29

    After many years of dreaming to have this first barbershop, it has finally come true. We are proud to announce that “The Good Barbers” has opened its doors for the first time at Alfred-Escher Strasse 66, 8002 Zürich, and this marks the beginning of our story.

    This dream involved many conversations, research and experience gained by working in some of the best barbershops located in Madrid, London and Zurich. We come from a family of entrepreneurs and have always had in mind that we should be taking risks whilst carefully deciding what the best business concept should be for this city that we call home.

    Hair Products for men We were clear that this business should be built with the following core foundations:

    - Tailored experience

    - Special care for the hygiene

    - Relaxing environment

    - Quality service, products and infrastructure


    With that in mind, one of the most important next steps was to find the first location for our business, we wanted it to be in the city, with good light and in a vibrant area. This search was found to be very challenging as we were not able to offer to the landlords any past record of us being successful as a company, and therefore it was the step that took us the longest to achieve. Thankfully, our chance arrived, and we were able to find a dream location for our business, it had everything we were looking for and more! Two stories, corner location, business hub, floor to ceiling windows…

    Once we were told we got this property, it was time to celebrate! But most importantly, it was time to start bringing to life all these concepts we had been discussing, creating, and modifying throughout these years. Thanks to all the preparation work we did; it was clear what the next steps were and how to execute them.

    Not to bore you with many details, but just to name a few of the concepts we had to now bring to life: furniture, company creation, suppliers, point of sale, software, webpage, talent… It took us many hours of thinking and execution, but we had a goal in mind all along, and it was to open our doors on March 1st, 2022. With project management skills, help from our loved ones and huge amounts of effort, we finally made it! And what a joyful moment it was to see the first client going into the barbershop the first day…


    We would like to take this opportunity, in our first blog post, to thank all of you who have supported us through this journey and also to all our clients who have been coming in or are planning to do so, and therefore giving us a chance. We know it’s challenging to trust a barbershop that has just opened with your hair, beard and facial needs and therefore why we are especially thankful to all of you.

    For any new customers, there is a ongoing offer of 15% discount in your first booking when done online. This offer lasts until 15th April 2022 and includes all services we offer. Definitely an offer not to miss out and that hopefully will bring an extra incentive to you for trying us out. We will do our best to give you a unique service experience in the best barbershop environment you will find in town.

    This is just the beginning of our dream, and we would love to continue sharing it with you all via our 1:1 appointments, social media (Instagram: the_good_barbers / Facebook: thegoodbarbersag) and through this blog.

    Your barbershop of reference in Zürich,

    The Good Barbers.

    ReplyDelete
  4. fgfgf25 April 2022 at 01:07

    What is an SMM panel?
    An SMM panel is an online shop that offers SMM services at affordable prices. indian smm panel

    What kinds of SMM services do you provide here?
    There are many types of SMM services available on our panel: likes, followers, views, etc.

    Are SMM services on this panel safe to buy?
    Our SMM services are totally safe to use, you won’t lose your accounts.

    A mass order — how does it work?
    You can place multiple orders with different links at once using the mass order feature

    What is Drip-feed?
    Grow your accounts as fast as you want with the help of Drip-feed. How it works: let’s say you want 2000 likes on your post. Instead of getting all 2000 at once, you can get 200 each day for 10 days.

    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

Autonomous Cars

The Problem with Self-Driving Cars Every year, so many people die in car accidents, most of them caused because of the driver's negligence. Exorbitant amounts of money are spent just to fund awareness campaigns and stop people from “drinking and driving”. All of this after the fact that the technology for self-driving cars is in the last stages of development. Why are self-driving cars not the next big thing yet? Companies like Tesla, Uber and heck, even Google are racing to be the next innovator of autonomous cars. “This is stupid… Obviously, the cars are expensive.” See that’s the point, these cars are not ridiculously expensive (at least not for people who own an iPhone X). “Well then we obviously don’t have the requisite technology” That is partially true but trust me, the cars are way closer technology-wise than you may think. The biggest problem with autonomous cars is (insert drumroll) “A Moral Dilemma”. Disappointed? Just hear me out. Imagine ...
Post a Comment
Read more

SETS, RELATIONS & FUNCTIONS

SETS, RELATIONS & FUNCTIONS Sets are a fundamental part of mathematics and it’s knowledge is very important in present. It defines the concepts of relation and functions. These functions are also very essential for present day maths. SETS Sets are denoted by capital letters. They are similar to matrices whose elements are denoted by small letters. But in sets an element comes only at once. Sets are matrices which give a sense of belonging. This sense of belongingness is represented by  ∈   .We can write anything in a set like rivers of India, Wonders of the World .etc.  For an example let there be a set of positive single digit. Let the set be denoted as A Therefore, 8 ∈ A  Also we can write, 17 ∈ A Set can be represented by two types  ROSTER In roster form we write elements in curly brackets and separate them with comma.  If there be set of positive integers less than 10. Therefore the set will be {1,2,3,4,5,6,7,8,9}  SE...
1 comment
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

Android Versions Named After Sweet

Have you ever thought why are Android versions always named after sweet names ?? Everytime a new Android version is launched its name is kept after a sweet name. Many people have researched about this topic and many have asked Google also. Have you ever tried to find out the core reason behind this? If not then you would find the answer here . First of all let us first see what Google says about this : In 2008 i.e. the year when Android was launched a reporter asked the reason for the same. At that time Google said “It’s kind of like an internal team thing, and we prefer to be a little bit — how should I say — a bit inscrutable in the matter, I’ll say,” said Randall Sarafa, a Google spokesman. “The obvious thing is that, yeah, the Android platform releases, they go by dessert names and by alphabetical order for the most part."
14 comments
Read more