Similarity and Architecture

We often compare and contrast things around us.  Brand X is better than Brand Y, Actress 1 is more beautiful than Actress 2, Usain Bolt is a faster runner compared to most athletes.

We are also fond of people or things with similarities. We are keen in observing people who look alike, we have a habit of collecting similar things of different colors (or sizes), and we even collect gadgets from a single manufacturer.

celebrity-look-alikes1

Similar things are everywhere. There are cartoon characters that are similar in some ways.  Those who do not recognize them would mistake them as family despite their different origins.  Buu and Patrick, for example, are like “uncles”, yet Buu was a violent alien, while Patrick has always been an amiable and friendly Starfish.
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Introduction to Similarity

In layman’s language, we say that two objects are similar if, in some way, they share certain characteristics. For example, we can say that two flowers are similar if they have the same number of petals and they have the same color, although, they might be different flowers.

Are Buu and Patrick similar?

Mathematically, similarity is quite different. In mathematics, we say that two objects are similar if they have “the same shape, but not necessarily have the same size.”

Now what does that exactly mean?

Similarity is an enlargement or reduction of objects.  A picture, for instance, may be enlarged or reduced in two ways. One way is stretching/shrinking it in proportion, and the other stretching/shrinking it horizontally or vertically.  When we say enlargement/reduction by proportion, we mean that if we want to increase/decrease the length by any percentage, we also increase/decrease the width by a similar percentage.

We can easily see that enlargement/reduction of pictures not in disproportion as shown below gives us a somewhat stretched picture. The second and the third picture in the first figure below are stretched horizontally and vertically, respectively.

This means that if we want to preserve the appearance of our picture, we must enlarge or reduce it in proportion.  The second figure is the proportional enlargement of the original photo.

In mathematics, we can only say that two objects are similar if their measurements are proportional. » Read more

Mathematics in Microsoft Office

There are many people who are allergic with mathematics, but most of the time, mathematics appears incognito in places where we don’t expect them to be.  One perfect example is the Microsoft Office Package.We know the MS Excel is dedicated to mathematical computations, but what about MS Word or PowerPoint?  Can we find mathematics in both applications?

Enumerated below are the mathematics hidden in Microsoft Office. Regarding the mathematics found in MS Excel, we will discuss more about them in later tutorials.

1. Equations (Word). In the Insert menu of MS Word, you can see the Equation icon located at the extreme right hand side of the toolbar. This contains several built-in mathematical equations and formulas such as area of the circle and binomial theorem.

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