In the last factoid, we talked about languages - most languages that we speak (or write) are vague, which means that we don't have to say things very exactly, and still others will understand what we mean. Programming languages on the other hand are precise and things have to be written very exactly. The most exact language that we use is called maths, which is the subject of today's factoid.
Numbers are the first thing we learn in maths.
We all use numbers in our daily lives. The first thing we learn is 1, 2, 3, 4, ... - these numbers are called natural numbers. When we use numbers to count things, like 3 apples or 5 books, we call the numbers as cardinal numbers. When we use numbers to talk about an order - like the second (2nd) book on the shelf or the fifth (5th) student from the left in a row of students, they are called ordinal numbers.
Note that we write numbers starting with the smallest number and increasing from left to right.
In the following list, which sentences use cardinal numbers and which use ordinal numbers?
Question 1:
a) I had two apples for breakfast.
b) Can you please get me the fifth book on the top shelf?
c) I want you to write six sentences about spices.
d) I want three students to step forward.
e) Fourth is the fourth word in this sentence. It was also the first.
After several years of using natural numbers, people realized the need for one additional number to represent nothing - zero. So, we now have 0, 1, 2, 3, 4, ... which are called whole numbers.
When we deal with numbers and operations between numbers, we are studying arithmetic.
When we go beyond actual numbers and start dealing with letters to represent numbers and start performing operations on those symbols, we are now studying a topic in maths called algebra.
Another thing we learn in math is about objects in space - this includes things like points, lines, curves, squares, rectangles, circles, and even volumes like a sphere or a cube. These are studied in the subject of geometry.
Geometry deals with lengths - such as the length of a line, or the side of a square or the radius of a circle.
Geometry also deals with angles - if we take a line and turn it around one point, we get an angle. A special kind of angle that is formed between two perpendicular lines is called a right angle. A triangle that has one of its angle as a right angle is called a right angled triangle or a right triangle.
Angles have special properties, especially when studies as an angle in a right angled triangle. This study of the properties of angles is called trigonometry.
We then study what happens when numbers change - how does one number change when another number changes - for example, if a car is going down a road, how does the position of the car change with time? We study such matters in a math topic called calculus or analysis.
As we learn these subjects, we will see that all these topics are actually 'cheating' us! We will see algebra in geometry, we will see geometry in trigonometry. We will see calculus using geometry, algebra and trigonometry. At the end, all of these are just math - different forms of the same thing. We will learn about each of these things in future factoids.
That ends factoid #2 that introduces the different subjects in math.
Numbers are the first thing we learn in maths.
We all use numbers in our daily lives. The first thing we learn is 1, 2, 3, 4, ... - these numbers are called natural numbers. When we use numbers to count things, like 3 apples or 5 books, we call the numbers as cardinal numbers. When we use numbers to talk about an order - like the second (2nd) book on the shelf or the fifth (5th) student from the left in a row of students, they are called ordinal numbers.
Note that we write numbers starting with the smallest number and increasing from left to right.
In the following list, which sentences use cardinal numbers and which use ordinal numbers?
Question 1:
a) I had two apples for breakfast.
b) Can you please get me the fifth book on the top shelf?
c) I want you to write six sentences about spices.
d) I want three students to step forward.
e) Fourth is the fourth word in this sentence. It was also the first.
After several years of using natural numbers, people realized the need for one additional number to represent nothing - zero. So, we now have 0, 1, 2, 3, 4, ... which are called whole numbers.
When we deal with numbers and operations between numbers, we are studying arithmetic.
When we go beyond actual numbers and start dealing with letters to represent numbers and start performing operations on those symbols, we are now studying a topic in maths called algebra.
Geometry deals with lengths - such as the length of a line, or the side of a square or the radius of a circle.
Geometry also deals with angles - if we take a line and turn it around one point, we get an angle. A special kind of angle that is formed between two perpendicular lines is called a right angle. A triangle that has one of its angle as a right angle is called a right angled triangle or a right triangle.
Angles have special properties, especially when studies as an angle in a right angled triangle. This study of the properties of angles is called trigonometry.
We then study what happens when numbers change - how does one number change when another number changes - for example, if a car is going down a road, how does the position of the car change with time? We study such matters in a math topic called calculus or analysis.
As we learn these subjects, we will see that all these topics are actually 'cheating' us! We will see algebra in geometry, we will see geometry in trigonometry. We will see calculus using geometry, algebra and trigonometry. At the end, all of these are just math - different forms of the same thing. We will learn about each of these things in future factoids.
That ends factoid #2 that introduces the different subjects in math.
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