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He discovered the all important Euler's Rule often referred to as Euler's Formula.
"Legend" usually refers to a text description. This is often used in graphs; for example, if you have several lines in a line graph, to describe what each line represents.
In any given set, the mode is the number that appears most often. If no number appears more frequently than any other, there is no mode. Ex. (10, 17, 20, 45, 68) This set has no mode.
The mode is the number that appears the most often. In this case it is 57.
The palimage of a number is the number obtained by reversing the order of its digits. For the number 354, the palimage would be 453. This is achieved by flipping the order of the digits from left to right.