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Consider a curve consisting of segments joining the points ... , where ... and ... . The region under this curve is broken into triangular pieces by extending the segments to the ... axis. Each extended segment projects onto a segment of length 1 on the ... axis because ... . You can align these triangles one on top of the other above the interval [0,1] on the ... axis using the "align" slider. You can control the constant ... using the "triangles per unit length" slider. Let ... . As ... and ... tend to infinity, the curve approaches the exponential curve ... . The "total length" slider controls the length of the ... interval. As the total length tends to infinity, the aligned triangles fill the unit square of area 1.
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