アドベンチャー数学　(Adventures in Math Class)

When developers are constructing houses, they must account for the roof. When constructing these roofs, the word pitch is used to assess the incline.  The term "pitch" is another type of measurement that is expressed when using slope. Like grade, it determines the steepness of a slope, but instead of measuring roads, pitch measures the steepness of roofs. Like grade and slope, to determining pitch is quite simple. You take the rise over run. When finding the angle of elevation of a roof when given its pitch, you simply take the inverse tangent and multiply it by the pitch. For example, a terracotta roof vertically "rises" 11 inches for every 18 inches horizontally "run". This means the pitch of the roof would be 11/18. What would the angle of elevation of the roof be? To solve this problem and find the angle of elevation, you simply take the inverse tangent and multiply it by the pitch. If following steps above, you should get the answer...

Today I'll be explaining grades of roads. Determining the correct grade of the road on a highway is extremely important to the safety of the motorists and drivers who drive on a certain road with a grade. The grade of a road is determined by the simple ratio of "rise over run." The grade  indicates how long you must travel up or down a road for a vertical rise or drop of a foot.  The rise is the change in vertical distance and the run is the change in horizontal distance. In short, the grade of roads are measured by the slope or incline of distance traveled. When you see grade signs on the sides of roads or highways, they're expressed in percentages. "x%" grades show the percentage of grade the road has. To find the percentage of the road, you simply multiply the decimal grade by "100".  Grade and slope are very closely related. In terms of finding the incline or slope of a road, they both measure the steepness. The slope shows the direct...

While researching the Menger Sponge, I was truly fascinated and didn't know that such a cool fractal existed! The fractal dimensions of the Menger Sponge are endless with an infinite number of cavity holes ~ almost like windows or a giant super city! When actually looking at this type of fractal, it reminded me very much of the once standing Kowloon Walled City in Hong Kong due to the endless amounts of windows or spaces left open in the sponge. The formation of the sponge starts with the splitting into 27 identical cubes. The center cube of all six sides is then removed which leaves 20 cubes. ( 8 cubes on the front face, 8 on the back, and then 4 in between).  The sponge exemplifies the attributes of self-similarity which is shown that similar copies of this type of fractal can be found in the original object just at smaller scales.