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Math Lesson 15.6.1 - Geometry Background
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Welcome to our Math lesson on Geometry Background, this is the first lesson of our suite of math lessons covering the topic of Circle Graphs, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Geometry Background
In this part of the tutorial, we will provide some useful information about circles. They will in no way eclipse the geometry tutorials in future chapters where all related concepts will be covered more extensively.
By definition, a circle is the set of all points that have the same distance from a fixed point called 'centre'.
We express the centre of a circle by the letter O (or sometimes C) and the common distance called radius by the letter R (or sometimes r). Given this description, it is clear that a radius has a single centre but an infinity number of radii, as each of them represents the shortest path that connects the centre and a given point of the circle.
Another important feature of circles is the diameter D, which represents the longest segment we can draw to connect two points of the circle. The diameter is twice the radius in length, i.e. D = 2r. For example, in the figure below the segment MN is a diameter.
The definition says "the set of points" but you can imagine a set of an infinite number of points that are close to each other to the point that the spaces between them become undetectable. In this way, it is easy to conclude that the set of points the definition refers to, is nothing more but a line - more precisely, a closed curve that surrounds the centre O, as shown in the figure below.
We must highlight here the fact that a circle includes only the points that belong to the closed line, not all points that are in the interior of the shape. Imagine having a circular garden surrounded by a wall. The circle here includes the wall only, not the garden.
The focus of this tutorial is not on the general features of a circle (perimeter, area, etc.) but on the relationship between the coordinates of any point on the circle. Therefore, we will put all circles we will deal with, in a coordinate system. The easiest case is when the centre of the circle corresponds to the origin of coordinates, as shown in the figure below.
It is easy to see that the radius of the circle above is 6 units and the origin is at (0, 0). In the next paragraphs, we will explain how to deal numerically with more challenging circles.
You have reached the end of Math lesson 15.6.1 Geometry Background. There are 5 lessons in this physics tutorial covering Circle Graphs, you can access all the lessons from this tutorial below.
More Circle Graphs Lessons and Learning Resources
Whats next?
Enjoy the "Geometry Background" math lesson? People who liked the "Circle Graphs lesson found the following resources useful:
- Geometry Feedback. Helps other - Leave a rating for this geometry (see below)
- Types of Graphs Math tutorial: Circle Graphs. Read the Circle Graphs math tutorial and build your math knowledge of Types of Graphs
- Types of Graphs Revision Notes: Circle Graphs. Print the notes so you can revise the key points covered in the math tutorial for Circle Graphs
- Types of Graphs Practice Questions: Circle Graphs. Test and improve your knowledge of Circle Graphs with example questins and answers
- Check your calculations for Types of Graphs questions with our excellent Types of Graphs calculators which contain full equations and calculations clearly displayed line by line. See the Types of Graphs Calculators by iCalculator™ below.
- Continuing learning types of graphs - read our next math tutorial: Transforming Graphs
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