Geometry, Angles, And Coordinates
This page is a review of the basic geometry concepts of angles, geometrical shapes, coordinates, and coordinate planes. These geometry concepts will be helpful to do LOGO programming effectively.
You have the concepts of angles already. For example, the corner of a dining table is an angle. This angle is called the right angle. It is also called 90 degrees angle. The angles can be larger than or smaller than 90 degrees. The following graph shows examples of angles smaller than 90 degrees.
Geometry Shapes and Their Exterior Angles
The websites uses the following geometrical shapes in the programming examples in the next units. The figure and the table below show the exterior angles and the interior angles for each polygon.
| POLYGON SHAPE | NUMBER OF SIDES | EXTERIOR ANGLE | INTERIOR ANGLE |
| Triangle | 3 | 360 ÷ 3 = 120° | 60° |
| Square | 4 | 360 ÷ 4 = 90° | 90° |
| Pentagon | 5 | 360 ÷ 5 = 72° | 108° |
| Hexagon | 6 | 360 ÷ 6 = 60° | 120° |
| Octagon | 8 | 360 ÷ 8 = 45° | 135° |
| Decagon | 10 | 360 ÷ 10 = 36° | 144° |
More About Angles
A full circle has 360 degrees as shown in the figure below. The figure below shows angles from 0 degrees to 360 degrees.
Introduction to Co-ordinates
When you start LOGO Program (see next chapter), the turtle appears at the center of a rectangular area. This position is called location (0,0). What is the meaning of (0,0)? To understand this, we will introduce what is called coordinates and Coordinate Geometry.
The above figure shows one horizontal line called X-axis and one vertical line called Y-axis. The horizontal direction is the X-direction and vertical direction is Y-direction. The X-axis and Y-axis cross each other in the center. This cross point is called the Origin. At the origin, the X-value is ‘0’ and the Y-value is ‘0’. Therefore, the origin is denoted by (0,0), where the first ‘0’ in the parenthesis is the X-value and the second ‘0’ is the Y-value. These numbers (0,0) are the coordinates of the Origin. The blue rectangular box in the figure above is an example of a coordinate plane. Below are more details of the coordinate plane, the Origin, the quadrants, and the x-axis and y-axis.
The Coordinate Plane
A coordinate plane is like graph paper. The figure below shows one horizontal line in the middle of the graph paper. This horizontal line is called the x-axis. There is one vertical line in the middle of the graph paper, which is called the y-axis. The horizontal direction is the X-direction and the vertical direction is the Y-direction. The x-axis and y-axis are perpendicular (right angle) to each other. The point where the x-axis crosses the y-axis is called the origin. At the origin, the x-value is ‘0’ and the y-value is zero. Therefore, the origin is denoted by (0,0), where the first ‘0’ is the x-value and the second ‘0’ is the y-value.
Coordinates
What is the meaning of (0,0)? To understand this, we will introduce what is called co-ordinates. The coordinate (0,0) is called the coordinates of origin. At origin, both x and y equal zero. On the x-axis, there is a scale that goes from zero at the origin to a higher positive number in the right direction and it goes from zero at the origin to a higher negative number in the left direction. Similarly, there is a scale on the y-axis that goes from zero to a higher positive number in the up direction and from zero to a higher negative number in the down direction. See the figure below.
The figure below shows a coordinate plane with the x-axis and y-axis and the horizontal lines and vertical lines spaced at a distance of 20. The figure also shows a point on the coordinate plane with coordinates of (60,100) in quadrant-1, (-100,+100) in quadrant-2, (-60,-40) in quadrant-3, and (+20,-40) in quadrant-4.
To explore further, check this link below.
<a href=”https://www.math.net/coordinate-plane“>
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