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.
More from Leonhard Euler
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.
Leonhard EulerRead
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.
Leonhard EulerRead
Similar quotes
I take no pleasure in the fact that the scientific predictions Iβve relayed to popular audiences turn out to be true.
Al GoreRead
That is the way of the scientist. He will spend thirty years in building up a mountain range of facts with the intent to prove a certain theory; then he is so happy with his achievement that as a rule he overlooks the main chief fact of all-that all his accumulation proves an entirely different thing.
Mark TwainRead
The evidence for human-made climate change is overwhelming.
James HansenRead
When I started working with NASA in 1989 as part of a mission to send spacecraft to Pluto, I knew it would take at least 10-15 years to see results of my efforts.
Alan SternRead
One of the liberating effects of science fiction when I was a teenager was precisely its ability to tune me into all sorts of strange data and make me realize that I wasnβt as totally isolated in perceiving the world as being monstrous and crazy
William GibsonRead
At one point consciousness-altering devices like the microscope and telescope were criminalized for exactly the same reasons that psychedelic plants were banned in later years. They allow us to peer into bits and zones of Chaos.
Timothy LearyRead