ÿþM i c r o s o f t W o r d - I M C 2 0 1 1 w e b s o l u t i o n s
... solutions given here have been extended. In some cases we give alternative solutions, and we have included some Extension Problems for further investigations. The Intermediate Mathematical Challenge (IMC) is a multiple choice contest, in which you are presented with five alternative answers, of whic ...
... solutions given here have been extended. In some cases we give alternative solutions, and we have included some Extension Problems for further investigations. The Intermediate Mathematical Challenge (IMC) is a multiple choice contest, in which you are presented with five alternative answers, of whic ...
Writing Percents as a Decimal or Fraction Convert from a percent to
... increase the amount of octane. How many gallons of gasoline can be treated with an 8 ounce bottle of isopropyl alcohol? Set up the proportion. ...
... increase the amount of octane. How many gallons of gasoline can be treated with an 8 ounce bottle of isopropyl alcohol? Set up the proportion. ...
An Investigation Relating Square and Triangular Numbers
... The output showed that many squares “d” have different representations as sums of three triangular numbers. I have included only a few examples of this in the above table, namely for the squares d equal to 49 and 64 and 225. In fact, I was struck by the proliferation of the different ways that a squ ...
... The output showed that many squares “d” have different representations as sums of three triangular numbers. I have included only a few examples of this in the above table, namely for the squares d equal to 49 and 64 and 225. In fact, I was struck by the proliferation of the different ways that a squ ...
Mathematics and architecture
Mathematics and architecture are related, since, as with other arts, architects use mathematics to shape and sometimes to decorate buildings.In ancient Greece, buildings were laid out with specific proportions. In Islamic architecture, geometric shapes and geometric tiling patterns are used. The pyramids of ancient Egypt have mathematical proportions. Hindu temples have a fractal-like structure where parts resemble the whole.In Renaissance architecture, symmetry and proportion were deliberately emphasized.In the twentieth century, styles such as modern architecture and Deconstructivism explored different geometries to achieve desired effects.