Pedagogy X

Pedagogy is a book designed to help students earn H1. It is divided into the sections Breasoning (X, Y and Z dimensions of objects), Rebreasoning (actions described as touching relationships), Breathsoning (human judgement of the object), Rebreathsoning (human judgement of the verb), Space (room, part of room and direction), and Time (time to prepare, time to do and time to finish).
It is necessary to generally think of a set of algorithms (an algorithm is a logical set of instructions) and specifically think of a breasoning, which is a summary of each algorithm. This is a sentence with a subject, verb and object. Also, breasonings have another meaning, which are the X, Y, Z dimensions of the subject and object in the sentence.
This chapter will not examine an algorithm which has an X dimension described as part of it, but one which contributes to describing the X dimension.
The following algorithm shows how the X dimension can be calculated in terms of calculating the angle necessary to kick a goal in. 1. goalangle(PlayerX, PlayerY, GoalLeftX, GoalRightX, GoalY, GoalAngleDegrees) :-
2. CentreOfGoal is GoalRightX – GoalLeftX,
3. Opposite is CentreOfGoal – PlayerX,
4. Adjacent is GoalY – PlayerY,
5. GoalAngleRadians is atan(Opposite / Adjacent),
6. GoalAngleDegrees is (GoalAngleRadians / (2 * 3.1459265)) * 360.
Line 1: Note: Suppose we have a triangle ∆ABC, in which ∟ABC is a right angle. DE is collinear with (runs along) BC, in the order BDCE.
Goalangle/6 takes the X and Y co-ordinates of the football player (A), the X co-ordinate of the left (D) and right hand side (E) of the goals, and the Y co-ordinate of the goals, and returns BAC, which is GoalAngleDegrees (which is the angle the player turns right to kick a goal through the centre of the goals, C).
Line 2: The X co-ordinate CentreOfGoal (C) is calculated by subtracting GoalLeftX (D) from GoalRightX (E).
Line 3: The Opposite side (BC) is calculated by subtracting PlayerX (B) from CentreOfFGoal (C).
Line 4: The Adjacent side (AB) is calculated by subtracting PlayerY (B) from GoalY (A).
Line 5: GoalAngleRadians is calculated using the formula tan(GoalAngleRadians) = Opposite / Adjacent where Opposite and Adjacent are opposite and adjacent sides of the angle GoalAngleRadians in the triangle. To find GoalAngleRadians by itself, we apply arctan() to both sides of the formula. So, GoalAngleRadians = arctan(Opposite / Adjacent).
Line 6: GoalAngleRadians is converted to GoalAngleDegrees using the formula GoalAngleDegrees = (GoalAngleRadians / (2 * pi)) * 360, where pi = 3.1459265. We divide GoalAngleRadians by the number of radians in a circle, to find the fraction of the circle the angle takes up. Then, we multiply it by 360 because we want to calculate how many of the 360 degrees in a circle the angle takes up, or GoalAngleDegrees.