For since the fabric of the universe is most perfect and the work of a most wise Creator, nothing at all takes place in the universe in which some rule of maximum or minimum does not appear.
Leonhard EulerRead
After exponential quantities the circular functions, sine and cosine, should be considered because they arise when imaginary quantities are involved in the exponential.
Interpretation
What this quote means
Euler emphasizes the importance of sine and cosine functions in relation to exponential functions, especially in the context of imaginary numbers.
In this quote, Leonhard Euler highlights the connection between exponential functions and circular functions, specifically sine and cosine. He points out that these trigonometric functions become significant when dealing with imaginary quantities, as they provide a way to represent complex numbers in a more manageable form, illustrating the deep relationships in mathematics between different areas such as complex analysis and trigonometry.
Themes
ExponentialSineCosineImaginaryFunctions
In practice
Example use cases
In a mathematics lecture explaining complex numbers, this quote can be used to highlight the role of trigonometric functions.
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All quotes βTo those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be.
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Notable enough, however, are the controversies over the series 1 - 1 + 1 - 1 + 1 - ... whose sum was given by Leibniz as 1/2, although others disagree. ... Understanding of this question is to be sought in the word "sum"; this idea, if thus conceived - namely, the sum of a series is said to be that quantity to which it is brought closer as more terms of the series are taken - has relevance only for convergent series, and we should in general give up the idea of sum for divergent series.
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