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Golden
Ratio and
Golden Rectangle
The Golden Ratio - also known as the ‘divine proportion’ or ‘golden mean’ - is the ratio 1.61803399…:1 (‘phi’). If you construct a rectangle with sides in this ratio, and divide it into a square and a smaller rectangle, the sides of the smaller rectangle will be in the same proportion as the original rectangle. Such a rectangle is called a Golden Rectangle. Both the Golden Ratio and the Golden Rectangle have been used in art and architecture across the ages.
Ancient Egyptians ascribed magical properties to this ratio, and used it in the design of their pyramids. If we take a cross-section of the Great Pyramid, we get a right triangle. The ratio of the slant height to the distance from ground centre is very close to the Golden Ratio.
Pythagoras, the Greek geometer, proved that the Golden Ratio is the basis for proportions of the human figure. This had a tremendous effect on Greek art and architecture, and a lot of their construction was based upon this proportion. The most famous of these buildings is the Parthenon.
Math Games for Everyday Situations
Dhobi Math
Calculate how much you need to pay the dhobi – even more fun if he charges different amounts for different kinds of clothes!
Dividing Fairly Math
Investigate how to divide a pizza equally, and explain the logic to siblings and friends.
Stock Market Math
Keep an imaginary portfolio in the stock market, and track its movements.
Arriving on Time Math
Calculate and record the average speed one can travel at in the city (record the distance travelled using your car’s meter, note the time taken for a few trips to get to an average). Before travelling, look up a map, estimate the distance, and the time you will need to get there, and therefore the time that you should leave home. The analysis can take time-of-day into account (average speed is lower at rush hour).
Traffic Jam Math
Count cars while stuck in a traffic jam. Or, estimate the number of cars stuck in the jam.
Sale Math
Calculate how much money you saved by shopping at a sale.
Recipe Math
Calculate and measure out ingredients for a recipe you’re cooking for a number that’s different from the one specified in the recipe.
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