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Apr
19
answered If there are obvious things, why should we prove them?
Apr
1
comment How do you find the general solution to a higher order nonhomogeneous differential equation?
Is this a question about the software product Mathematica?
Mar
15
comment Why are the axes in coordinate geometry perperndicular?
It may be of interest to note that Descartes did not use perpendicular axes in his Geometry. He used distances to given lines, the given lines being at whatever angles and sometimes more than two in number. So having coordinate axes at angles other than 90 degrees came first. Descartes used his method to solve a problem of Pappus that the ancients Greeks could not, and thus proved a new theorem.
Mar
15
comment Why are the axes in coordinate geometry perperndicular?
@Kartik Euclidean and non-euclidean geometries are not equivalent. Two coordinate geometries are. You just get different formulas with different coordinate systems, formulas for things like distance, translations, rotations. Some of these are simpler in one coordinate system than another.
Mar
15
comment Crazy $\int_0^\infty{_3F_2}\left(\begin{array}c\tfrac58,\tfrac58,\tfrac98\\\tfrac12,\tfrac{13}8\end{array}\middle|\ {-x}\right)^2\frac{dx}{\sqrt x}$
@ClaudeLeibovici, @VladimirReshetnikov Oops, I mistyped one of the coefficients. The answer I get is (25 MeijerG[{{-(1/8), 3/8, 3/8}, {9/8}}, {{1/8, 1/8, 5/8}, {-(5/8)}}, 1])/(32 Sqrt[2] Gamma[5/4]^2) with Integrate[HypergeometricPFQ[{5, 5, 9}/8, {4, 13}/8, -x]^2/Sqrt[x], {x, 0, Infinity}] on Mma V9.0.1. Sorry for the error.
Mar
13
comment Finding the point that a normal line goes through
@RickyMutschlechner Thanks for the accept. I wish you the best with the rest of the course.
Mar
11
comment I don't like Wolfram Alpha's evaluation of an integral
+1. You're more generous toward W|A than I would be. :) I would have said it was just wrong at $x = n\pi$, since the antiderivative is not differentiable at those points, no matter how sgn is defined. Since the integrand is continuous everywhere, there is an antiderivative that is differentiable everywhere, which of course you have given. The W|A antiderivative cannot be used to apply the Fundamental Theorem of Calculus, which seems a shortcoming worth pointing out. (W|A and Mathematica often give symbolic results that are only generically correct.)
Mar
11
comment Finding the point that a normal line goes through
@RickyMutschleckner You don't have to solve for $f$. It is given. See my answer for details.
Mar
11
answered Finding the point that a normal line goes through
Mar
11
comment Finding the point that a normal line goes through
Solve $f'(a) = -a/f(a)$. (Slope of tangent is negative reciprocal of radial line from origin.)
Mar
9
comment solving a trigonometric differential equation
This is covered in standard textbooks on differential equations. Perhaps it's in yours?
Jan
21
awarded  Necromancer
Jan
11
comment Why is Euclid's proof on the infinitude of primes considered a proof?
@MarcvanLeeuwen FWIW, Euclid used the word ἄπειρον, unbounded or infinite, sometimes in geometry (e.g. Post. 5), but not in this proposition. He used the word πλῆθος, multitude, which incidentally is the word used to define number. A number is a multitude of units. In IX.20, Euclid stated, "The prime numbers are more than any proposed multitude of prime numbers" -- he is just that close to saying a "number of prime numbers."
Dec
29
awarded  Yearling
Nov
3
comment Is Euclid's Fourth Postulate Redundant?
Yes, I meant why E. didn't make I.4 an axiom. Really, I wonder why he didn't make the ability to fit one figure on another an explicit axiom. Since he used it in a critical way in I.4 (and in I.8), on which most other props. are based, I don't think he could have thought it suspect, but we can't be sure what he believed. The ability to superpose figures might be argued to be implicit in C.N. 4, just as addition and subtraction of magnitudes are presumed in C.N. 1-3. It's better to prove a statement than assume it. So thought the Greeks, for E. was thus criticized for post. 5.
Nov
2
comment Is Euclid's Fourth Postulate Redundant?
Then I wonder that he didn't assume I.4.
Nov
2
comment Is Euclid's Fourth Postulate Redundant?
I wonder that Euclid did not apply the "method" of proof of prop. I.4 to prove Post. 4. That method is open to objection by modern standards, but if Euclid could use it on I.4, why not on the postulate?
Nov
2
revised How to calculate simple trigonometric problem
Added image
Nov
2
answered How to calculate simple trigonometric problem
Nov
2
comment How to calculate simple trigonometric problem
Or simply wolframalpha.com/input/?i=tan(sin%5E-1(1%2F3))