Wednesday, February 15, 2017

Famous Ratios and Ratios Used With No Thought.

Calculator, Three Dimensional, SymbolYesterday, 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.