# What Is The Trapezoid Rule In Hockey? [Updated!]

Hockey is one of the most popular sports in the world. In the U.S., it is played by more than four million people. It is an incredibly popular and competitive sport in the U.S., which is reflected by the large number of fans who follow the NHL (National Hockey League) while also competing in the sport themselves.

Even though hockey is a team sport, it is still often played by individuals. One of the most exciting things about the sport is the scoring, which is frequently tied to creativity and strategy. In order to improve your own game, you can use this blog post to educate yourself about the strategy and rules of hockey.

## What Is The Trapezoid Rule?

If you are not familiar with the trapezoid rule, here is a short explanation. The trapezoid rule allows you to calculate approximate values in situations where you do not have access to a calculator. The rule is so named because it is a combination of the trapezoid shape and the rule of arithmetic progression. It was originally developed for the approximation of the area under a curve (also known as an integral), and it can be used to determine the area of a curve or the values of a function at particular points.

## How Does It Work?

Let’s use the circumference of a circle as an example. The circumference of a circle is often used as a measure of area because it is easy to calculate. If you have a look at the formula for calculating the area of a circle, you will see that it is simply (pi x radius)(radius x 2). As you can imagine, this is rather tedious to do by hand, especially if you need to do it for many different radii. This is where the trapezoid rule comes in. Using this rule, you can estimate the area of a circle with any degree of accuracy (within 4%) simply by dividing the area into four equal sections like this. Remember: this is only an approximation, and it is not perfect.

The beauty of this rule is that you do not need to know the precise values of x and y to do it. You only need to know that the point (0,0) is at the very top left of your screen and the point (1,1) is at the very bottom right. So, in this case, the rule is as follows:

(0, 0)
(0.4, 0.4)
(0.8, 0.8)
(1, 1)

What this means is that, for any x in the closed interval [0, 1], you can find the corresponding y in [0, 1] such that this formula gives you the area under the curve from (0, 0) to (x, y). In this case, you can see that 0.4
(the x-coordinate of the point (0.4, 0.4))
corresponds to 0.8 (y coordinate of the point (0.8, 0.8)).

## The Application Of The Trapezoid Rule In Hockey

Let’s work through an example. Say you have a function that you need to determine the area under the curve for. In this case, we will use the hockey scoring system, which ranges from 0-5, and it is given by the formula s = (v – w) + (u – v) ∗ 5, where u, v, and w are the points (individual’s scores) at which you have reached. You can see that this is just like the circle example above, except that here we have three variables instead of two. We can use the trapezoid rule in order to find the area under the curve for s.

To apply the trapezoid rule, you will need to break up the integral into four pieces, like this:

(0,0)
(0.4, 0.4)
(0.8, 0.8)
(1.2, 0.8)
(1.6, 0.4)

Each of these pieces has an associated value, which you can find by using the formula given above.

This is actually a very similar process to what you would need to do in order to find the area under the curve for v – w. In that case, you would need to break up the integral into four pieces like this:

(0,0)
(0.4, 0.4)
(0.8, 0.8)
(1.2, 0.8)
(1.6, 0.4)
(2, 0.0)
(2.4, 0.4)
(2.8, 0.8)
(3.2, 0.8)
(3.6, 0.4)
(4, 0.0)
(4.4, 0.4)
(4.8, 0.8)
(5, 1.0)

What is important here is that you should be able to find the area under the curve for any function for which you know the values of u, v, and w. As long as you can do this, you will be able to use the area under the curve to determine the final score. So in this case, the trapezoid rule gives us the following values:

(0, 0)
(0.4, 0.4)
(0.8, 0.8)
(1.2, 0.8)
(1.6, 0.4)
(2, 0.0)
(2.4, 0.4)
(2.8, 0.8)
(3.2, 0.8)
(3.6, 0.4)
(4, 0.0)
(4.4, 0.4)
(4.8, 0.8)
(5, 1.0)

## Advanced Applications Of The Trapezoid Rule In Hockey

If you are an advanced user of the trapezoid rule, you can use it in even more complex situations. Say you have the following scenario: