Editing 2042: Rolle's Theorem
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==Explanation== | ==Explanation== | ||
− | + | {{incomplete|Go a little bit more into the explanation. Do NOT delete this tag too soon.}} | |
− | + | In mathematics a {{w|Differentiable function|differentiable function}} is a function whose derivative exists at each point in its domain. The derivative represents the slope of the corresponding graph which must be ''smooth'' in any point without any abrupt breaks or similar. In the case of this comic the slope starts with a positive value at point (a), then decreases until it reaches zero at point (c), and then smoothly turns to a negative value towards point (b). Only the area for positive x- and y-values are considered as the relevant domain. | |
− | + | In {{w|Differential calculus|differential calculus}} the derivative of a function f(x) is often noted as f'(x). The value f'(c)=0 here represents the value of the derivative of the function f(x) where x equals the value c. | |
− | + | A {{w|Theorem|theorem}} in mathematics is a statement that has been ''proven'' by former excepted statements like other theorems or even more substantial {{w|Axiom|axioms}}. Without a proper prove a statement is called a hypotheses. | |
− | Randall | + | To [[Randall]] it's trivial that a line starting with a slope upwards but then turning downwards to the same level must have, at least at one point in the middle, a slope of zero. |
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+ | This comic references the theorem in calculus {{w|Rolle's theorem}}, which is intuitively obvious but harder to prove than they seem. | ||
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+ | At the title text Randall mentions a line together with a ''coplanar'' circle. This simply means that those both two dimensional objects must lay in the same plane in a higher, three or more dimensional space. And by this means every line drawn through the center of a circle is just a diagonal which divides it into two equal parts. | ||
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+ | It is interesting to note that the theorem mentioned in the title text is already taken: even if this theorem is trivial, {{w|Proclus}} says that the first man who proved it was {{w|Thales of Miletus|Thales}}. Auctioning of {{w|Naming rights}}, also noted in the title text, refers to the practice of naming entertainment venues for companies which pay for the privilege, such as any of the three {{w|Red Bull Arena}}s or {{w|Quicken Loans Arena}}. | ||
==Transcript== | ==Transcript== | ||
:[A single framed picture shows a colored x-y-graph with a text above:] | :[A single framed picture shows a colored x-y-graph with a text above:] | ||
:'''Rolle's Theorem''' | :'''Rolle's Theorem''' | ||
− | : | + | :From Wikipedia, the Free Encyclopedia |
:Rolle's theorem states that any real, differentiable function that has the same value at two different points must have at least one "stationary point" between them where the slope is zero. | :Rolle's theorem states that any real, differentiable function that has the same value at two different points must have at least one "stationary point" between them where the slope is zero. | ||
− | :[The graph shows a sine like curve in blue intersecting the x-axis at points "a" and "b" marked in red while in the middle a point "c" has a vertical dashed green line to the apex and on top also in green f'(c)=0 is drawn with a horizontal | + | :[The graph shows a sine like curve in blue intersecting the x-axis at points "a" and "b" marked in red while in the middle a point "c" has a vertical dashed green line to the apex and on top also in green f'(c)=0 is drawn with a horizontal line. |
:[Caption below the frame:] | :[Caption below the frame:] | ||
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[[Category:Comics with color]] | [[Category:Comics with color]] | ||
[[Category:Line graphs]] | [[Category:Line graphs]] | ||
− | [[Category: | + | [[Category:Math]] |
[[Category:Wikipedia]] | [[Category:Wikipedia]] |