- 13 hours ago
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- 13 hours ago
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Source: spring-of-mathematics

One applications of Slope to explains puzzles and paradoxes -Triangle Dissection Paradox

"Below the two parts moved around - The partilisions are exactly the same, as those used above - From where "come" this hole?"One of the reason in this problem is the slope of the “hypotenuse” in figure 1 and figure 2 are different. (Image 2 - Click on imgae to see full size).

Also, The above two figures are rearrangements of each other, with the corresponding triangles and polyominoes having the same areas. Nevertheless, the bottom figure has an area one unit larger than the top figure (as indicated by the grid square containing the dot).The source of this apparent paradox is that the “hypotenuse” of the overall “triangle” is not a straight line, but consists of two broken segments. As a result, the “hypotenuse” of the top figure is slightly bent in, whereas the “hypotenuse” of the bottom figure is slightly bent out. The difference in the areas of these figures is then exactly the “extra” one unit. Explicitly, the area of triangular “hole” (0, 0), (8, 3), (13, 5) in the top figure is 1/2, as is the area of triangular “excess” (0, 0), (5, 2), (13, 5) in the bottom figure, for a total of one unit difference. Source: Triangle Dissection Paradox on Mathworld.wolfram.

Slope:In mathematics, theslopeor gradient of a line is a number that describes both the direction and the steepness of the line. Slope is often denoted by the letter m. Slope is calculated by finding the ratio of the “vertical change” to the “horizontal change” between (any) two distinct points on a line. Sometimes the ratio is expressed as a quotient (“rise over run”), giving the same number for every two distinct points on the same line. The rise of a road between two points is the difference between the altitude of the road at those two points, say y1 and y2, or in other words, the rise is (y2 − y1) = Δy. For relatively short distances - where the earth’s curvature may be neglected, the run is the difference in distance from a fixed point measured along a level, horizontal line, or in other words, the run is (x2 − x1) = Δx. Here the slope of the road between the two points is simply described as the ratio of the altitude change to the horizontal distance between any two points on the line.- Also, here are the direction of a line is either increasing, decreasing, horizontal or vertical:
- A line is increasing if it goes up from left to right. The slope is positive, i.e. m>0.

- A line is decreasing if it goes down from left to right. The slope is negative, i.e. m<0.- If a line is horizontal the slope is zero. This is a constant function.

- If a line is vertical the slope is undefined (see below).The steepness, incline, or grade of a line is measured by the absolute value of the slope. A slope with a greater absolute value indicates a steeper line - Source: Slope on Wikipedia

Image:Shared at http://imgur.com/lYy5b&Slope on Wikipedia

- 15 hours ago
- 58

Source: ashjpegTHEY ARE CRYSTAL GEMS

THEY DO NOT HAVE A RACE

THEY ARE NOT HUMAN

ONE IS A CREAM COLOR, ONE IS RED, AND THE OTHER IS PURPLE

NONE OF THE CRYSTAL GEMS ARE BLACK/WHITE/ASAIN/

HISPANIC OR ANYTHING ELSEIF YOU FEEL STEVEN UNIVERSE IS BEING RACIST

YOU ARE TAKING THINGS WAY TOO SERIOUSLY AND YOU NEED TO SIT DOWN AND REEVALUATE YOUR LIFE

- 15 hours ago
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- 15 hours ago
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### http://recursorsprite.tumblr.com/post/92469027158/alright-so-ive-seen-a-lot-of-discussion-on

Source: recursorspriteAlright so I’ve seen a lot of discussion on Sugilite’s character design, and I’ve mostly seem comparisons to gorillas (or the great ape from Dragon Ball Z), tarantulas and foo dogs. And I do agree that she does share certain characteristics with all of them. But there is actually one very obvious…

- 15 hours ago
- 2243