Game Design and Ratios.

  I downloaded a game which is designed to help students learn to work with ratios but I'm not sure its a good one.  The premise is the student is given a ratio such as three greens to one red and they have to connect them together with a finger drawn line.

I played it but it seemed just like any other fancy game. I'm not sure how it teaches ratios to students.  But ratios are often used in game design itself.

One type of ratio is a fixed ratio which is where the game designer sets up a ratio after so many repeated actions.  An example might be an extra charge after collecting 20 jewels.  This happens all the time and doesn't change, thus its fixed.

This ratio leads to a period where not much happens until the player decides to go after the goal.  Then the player will move as fast as possible to achieve the goal and getting the reward.

The other ratio is a variable ratio, where the number of action changes so it requires a different number every time to achieve a goal.  For instance, the number of enemy fighters shot down to get a new fighter of your own, changes each time.  The variable ratio encourages more regular activities without the pause associated with the fixed ratio.

Not all rewards are on a fixed or variable ratio.  The designer might choose to use a fixed interval where the player receives a reward.  It might be one reward for every hour played.  It stays the same.  Where as the designer might choose a variable interval where the time played varies before earning the reward.

In a sense the intervals are also a ratio.  Instead of 1 new protection for every 15 wizards dispatched, it might be 1 new protection every 20 minutes.  Its a ratio using time rather than objects.

In addition, the golden ratio plays an important part in game design.  The golden ratio (1:1.61) is used to create proper looking surroundings for the game itself.  So by applying this rule when creating the background, trees, etc, you get a more realistic look because this ratio is found throughout nature and we are used to seeing things that way.

The golden ratio is often used in by dividing the scene into thirds to get a rough idea of where to put things.  In some games, the first third line represents the horizon while the second third is the architecture line.  Other games use the first third line as a line while the second third is the eye height line for the characters.  The vertical lines express where the enemy stands and where the hero or your character stands. 

Again ratios.  I love that ratios are found in game design because there are so many resources out there to teach students game design.  What do you think.

Famous Ratios and Ratios Used With No Thought.

Yesterday, I let my mind wander.  It began with division before heading off to scales as in scale models, eventually settling on ratios.  There are several famous ratios we use in real life.  Mathematical things we don't even think about being ratios.

The most famous example is Pi.  Pi is defined as the ratio of the circumference to the radius of a circle.  How many times have you had students try to measure the circumference of a circle using a string that was later lined up against a ruler.  The ruler is also used to determine the radius.

This activity has lead to great  discussions on why their results are no where close to the actual number.  We've discussed stretch, lack of precise measurement, and all sorts of other issues.

The golden ratio is another famous one.  Basically it is the whole length/long part = long part/short part or approx. 1.618....  It appears in art, architecture,  geometry, and other areas.  This is even mentioned in Numb3rs and the Da Vinci Code.  It is said the golden ratio was used by the Egyptians while it was used by Da Vinci when he painted the Last Supper.  In addition, people who create labels for soda and such use it so the ratios look right on the bottles.

In addition, dentists use the golden ratio when fixing teeth.  Both Notre Dame and the Parthenon were built using the golden ratio.  There are more places you see it, in certain instruments or even with insects.  The golden ratio has a tremendous influence without our being aware of it. 

In the financial realm, there are many ratios used and the following are just two.
1. Price to earnings ratio which is used to determine if the price of a stock is reasonable.
2. Profit margins = Net income/sales.
I hadn't heard of these but if you are in business, you are likely to be quite familiar with them.

Even in maps, there are certain standard ratios found.  The USGS uses 11 different scales on their maps depending what the map is of.  If its of Puerto Rico, it will have a 1:20,000 ratio while the map of the United States is 1:1,000,000.  

Anytime you look at  road map, an atlas, or anything else that has a map, you are going to see a ratio which is often referred to as a map scale.  It might be 1 cm represents 20,000 cm or 1 inch represents 100 km.  It depends on how the scale is set up.

In addition, look at building plans whether for furniture or for houses.  They are all done to scale with a ratio such as 1:20, 1:50, or 1:100 in S.I. units or 1/4" or 1/8" for US units.  the 1/4" inch means 1/4" on the plan represents one foot when its built. 

All these ways and we don't give it a second thought we are using ratios.  We don't think about it at all.