Fibonacci

.Prime numbers

Fundamental Theory of arithmetic

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Bottle Fascination

Study the graphs below, these are just basic shapes, as we proceed onto harder shapes, explanations will be given.

Height in B increases rapidly with volume increase, howver since it has a low volume, it will result in the graph stopping after a while of steep increase. For B as its Volume at the bottom is large, its height increase is slow, however, its graph will be longer as its volume is the largest of the three.

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The bottles here as you can see (B AND F will

Result in opposite graphs.) As you goon further, you will discover that bottles with circular surfaces or straight sloping sides will result in bottles having curved graphs while bottles with jagged surfaces will have straight line graphs divided in sections in accordance to how many jagged sections

the bottle has. An example is shown below…

Reason as to why straight sloping surfaces have curve graphs can be explained when you imagine yourself as the water travelling upwards, in the jagged bottle, you will have to stop for a while before continuing your journey to the top, giving rise to the section seperated straight line graph. On the other hand, for the straight sloping sides, you will just have to travel without making any significant stop, thereby giving rise to a curved graph.

 This one's interesting, study it, understand it and come up with bottles and graphs of your own.

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