Timeline for When did coordinate plane "as we know it" come into play?
Current License: CC BY-SA 3.0
11 events
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| Jul 28, 2014 at 23:52 | history | edited | Francois Ziegler | CC BY-SA 3.0 |
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| Jul 28, 2014 at 11:36 | comment | added | Amir Asghari | I was worried that the distinction between input and output does not make sense.Happy it did, and thanks for clarifying your answer. | |
| Jul 28, 2014 at 10:41 | comment | added | Francois Ziegler | @AmirAsghari Aha, your input notion is subtler than I thought. I view Halley's whole paper as an exercise in juggling with (Shapiro's words) the "single equation" $$\frac{pdr\rho}{dr+d\rho-pr\rho}=f,$$ where all letters are alternately regarded as input or output. E.g. once it is seen that the focus or radius can be negative as output (when solved for), then it can be negative as input too. But I would agree that Halley is not fully consistent -- perhaps because he is in the process of overturning old habits, which die hard... | |
| Jul 28, 2014 at 5:19 | comment | added | Amir Asghari | Euler's Elements of Algebra is full of such use of letters. For example, he admits negative solution of equations, say x=-13, but after working out an equation of the form ax+by=c, in which a, b, and c represents positive numbers, writes: Now, if b is negative, and the equation has to form ax-by=c...!consider that how he bypasses the use of negatives as input. Basically, when he writes "if b is negative" he means "let the coefficient of y be negative". | |
| Jul 28, 2014 at 4:53 | comment | added | Amir Asghari | Dear Francois, your answer as usual is enlightening, but unfortunately this time, is not answer the question! Here are some reasons: (1) there is a big difference between a signed letter and a letter that admits signed numbers. (2) The so-called rules of signs is quite an aspect of "arithmetical algebra" in which letters stand for positive numbers. (3)ρ, in the formula you mentioned, is an example in which a letter can have a negative number as "output" rather than "input"... (to be continued) | |
| Jul 28, 2014 at 4:40 | comment | added | Todd Trimble | Meanwhile we do have a notion of "excellent ring". en.wikipedia.org/wiki/Excellent_ring So I guess all is not lost. | |
| Jul 28, 2014 at 3:34 | history | edited | Francois Ziegler | CC BY-SA 3.0 |
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| Jul 28, 2014 at 3:26 | history | edited | Francois Ziegler | CC BY-SA 3.0 |
Added Newton and Wallis
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| Jul 28, 2014 at 2:07 | comment | added | Charles Rezk | @TomLeinster Someday I hope to write a paper containing a definition of the form: "We say that a topological space is most excellent if ..." | |
| Jul 28, 2014 at 1:35 | comment | added | Tom Leinster | Imagine if someone nowadays wrote a paper whose title started "An instance of the Excellence of Modern ALGEBRA". You'd immediately dismiss them as a crank. Have we lost something? Or do we just prefer our titles not to sound like Bill and Ted? | |
| Jul 28, 2014 at 0:01 | history | answered | Francois Ziegler | CC BY-SA 3.0 |