It may be easier to produce the shapes in Illustrator or Paint Shop Pro or any one of a number of other drawing packages and use them to illustrate your lessons, but sometimes, some simple diagrams in Moodle will do a better job. Arcs are also easy to produce, but require some additional parameters.

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The same code structure used in circles create the basic shape, but the inclusion of a start and end point creates only the arc. However, notice where the 0 point is, not at the true North, but rather the East and run in an anti-clockwise direction. Note that the canvas is the size of the diameter nominated by the circle's parameters. Using circles and arcs as shown above is somewhat limiting. Each part of the picture though needs to be in its own space, and while this frame allows you to be creative, to a degree, there are some very hard and fast rules about using it.

All elements of a picture need to be located within the picture frame. Unexpected results occur when parts of an arc, for example, runs over the border of the frame. This is particularly true of lines, which we will get to next, and the consequences of that overstepping of the border can cause serious problems. NOTE: The brace is used to enclose each set of required starting point coordinates.

Inside each set of braces, another set of braces is used to isolate each set of coordinates from the other, and those coordinates use their proper brackets and backslash. Count the opening and closing brackets, be careful of the position,. Because of the frame size of px and the centre point of the circle in the mid-point of the frame, the px circle will be squashed. Unexpected results occur when sizes are not correct.

Using the picture frame, you can layer circles and lines over each other, or they can intersect. You may have to try to place the centre dot correctly , but the ordering of the elements in the image may have an impact. If the line is not noted properly then the parser will try to correctly draw the line but will not successfully complete it. This means that every image that needs be drawn will be drawn until it hits the error. When the error is being converted, it fails, so no subsequent image is drawn.

### Some examples

The 20,0 provides the starting coordinates for any line that comes after. In this case the start point is at 20pixels in the x axis and 0 pixels in the y axis. The starting point for all coordinates, 0,0, is the bottom left corner and they run in a clockwise manner. Do not confuse this with arcs. In this case, the inclination is 0 and the length is px. The next set of commands are the same, that is, the 20, are the coordinates of the next line.

The x co-ordinate is the 20, that is the distance to the right from the 0 point. The y co-ordinates is the distance from the bottom of the image. Whereas the first line started and ran on the bottom of the picture frame, the y co-ordinate starts at the pixel mark from the bottom of the image. The line, at pixels long and has no y slope. This creates a spread pair of parallel lines. While this explains the structure of a line, there is a couple of elements that you need to go through to do more with them.

There should be a square box tool, and there is, but unless it has something inside it, it does not display. Controlling angles is a little different. They involve a different perception, but not one that is unfamiliar. We have a point from which we want to draw a line that is on an angle.

The notation used at this point can be positive, positive or positive, negative or negative, positive or negative, negative. Think of it like a number plane or a graph, using directed numbers. The 0,0 point is in the centre, and we have four quadrants around it that give us one of the previously mentioned results. Essentially, what these points boil down to is that anything above the insertion point is a positive on the y axis, anything below is a negative. Anything to the left of the insertion point is a negative while everything to the right is a positive.

The co-ordinate alignment process in TeX is not that good that you can use one set of co-ords as a single starting point for all lines. The layering of each object varies because of the position of the previous object, so each object needs to be exactly placed.

This co-ord structure has a great deal of impact on intersecting lines, parallel lines and triangles. NOTE: Labeling this image, above-right, turned out to be fairly simple. Offsetting points by a few pixels at the start or end points of the lines proved a successful strategy. The X point proved a little more problematic, and took a number of adjustments before getting it right. Experience here will help. Combining lines and arcs is a serious challenge actually, on a number of levels.

### Your Answer

For example lets take an arc from the first page on circles. All elements in this drawing start in the same place. Each is layered, and properly placed on the canvas, and using the same co-ord to start makes it easy to control them. No matter the size of the arc, intersecting lines can all be drawn using the centre co-ords of the arc. Of all the drawing objects, it is actually triangles that present the most challenge.

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For example:. This triangle has been developed for a Trigonometry page - but the additional notation should provide insight into how you can use it. The hypotenuse is always the side that is opposite the right angle. The longest side is always the Hypotenuse. A Matrix is a rectangular array of numbers arranged in rows and columns which can be used to organize numeric information. Matrices can be used to predict trends and outcomes in real situations - i.

A matrix can be written and displayed like. The pipe, , and the full stop determine the line type for the vertical line. Equal and unequal matrices are simply matrices that either share or not share the same number of rows and columns. To be more precise, equal matrices share the same order and each element in the corresponding positions are equal. Anything else is unequal matrices. Actually equal and unequal matrices are constructed along similar lines, but have different shapes:. Addition and subtraction matrices are similar again, but the presentation is usually very different.

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## Art of Problem Solving

The problem comes when trying to mix labels into arrays. The lack of sophistication in the TeX Notation plays against it here. It is better to use the Moodle Fullscreen editor for this, to have a better idea of how the end product will look and to take advantage of the additional tools available.

Design decisions need occupy our attention for a while. We need a table of five rows and four columns. The first row is a header row, so the label is centred. The next row needs four columns, a blank cell to start and labels A, B and C. The next three rows are divided into two columns, with the labels, pies, pasties and sausage rolls in each row of the first column and the matrix resides in a merged set of columns there. So first the table:. While not a very good look, it can be made better by tweaking the table using the advanced settings and properties buttons and then you can tweak the matrix itself.

Things are not always as they seem, be aware, the "c" does not stand for "column", it actually stands for "centre". The columns are aligned by the letters l, for left, c for centre and r for right. Each column is spread across 50 pixels, so the value of 50 is entered into the alignment declaration. The plus sign before the value is used to "propogate" or to force the value across the whole matrix, but is not used when wanting to separate only one column.

To set the rows is a little more problematic. The capital letter C sets the vertical alignment to the centre, B is for baseline, but that does not guarantee that the numbers will appear on the base line, and there does not appear to be any third value. The plus sign and following value sets the height of all rows to the number given. In this I have given it a value of 25 pixels for the entire matrix.

If there were four or five rows, the same height requirement is made. The order things appear is also important. If you change the order of these settings, they will either not work at all, or will not render as you expect them to. If something does not work properly, then check to make sure you have the right order first. The rule for performing operations on matrices is that they must be equal matrices. Since its development in , LaTeX has become popular in disciplines such as mathematics, physics and computer science.

## Latex Example Math

Proponents embrace LaTeX because of the total control it offers for document layout, or because it represents a blow to commercial software developers, particularly Microsoft. Others regard the software as too complicated for all but the most demanding of tasks. A study M.

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