Differences

This shows you the differences between two versions of the page.

--- math [2020/09/26 22:01] – raju
+++ math [2023/08/12 04:40] (current) – [pages in this wiki] raju
@@ Line 12: / Line 12: @@
 Derivation of the reverse equation:
 \begin{align*}
-t & = r \sqrt{\frac{n-2}{1-r^2}} \\
+& t = r \sqrt{\frac{n-2}{1-r^2}} & \\
-\frac{t^2}{r^2} & = \frac{n-2}{1-r^2} \\
+& \frac{t^2}{r^2} = \frac{n-2}{1-r^2} & \\
-\frac{t^2}{n-2} & = \frac{r^2}{1-r^2} \\
+& \frac{t^2}{n-2} = \frac{r^2}{1-r^2} & \\
-\frac{t^2}{t^2 + n-2} & = r^2 \\
+& \frac{t^2}{t^2 + n-2} = r^2 & \\
-r & = \sqrt{\frac{t^2}{t^2 + n-2}}
+& r = \sqrt{\frac{t^2}{t^2 + n-2}} &
 \end{align*}
+See also:
+  * https://stackoverflow.com/questions/2632628/left-align-block-of-equations - shows a trick to left align an equation array
 ==== sec(x) + tan(x) ====
@@ Line 27: / Line 29: @@
 I came across this simplification while reading https://liorsinai.github.io/mathematics/2020/08/27/secant-mercator.html which talks about the integral of the secant which in turn has applications in Mercator map.
+==== pages in this wiki ====
+  * [[fibonacci sequence]]
+  * [[Leibniz integral rule]]
+==== links I came across ====
+  * What is the formula for sum of the p-th powers of the first n positive integers?
+    * Use Faulhaber's formula in described in https://en.wikipedia.org/wiki/Faulhaber%27s_formula
+    * The formula involves binomial coefficients and Bernoulli numbers.
+    * See also: https://www.johndcook.com/blog/2016/12/31/sums-of-consecutive-powers/
+==== pages with math outside of this wiki ====
+use cases | to copy paste syntax
+  * https://liorsinai.github.io/mathematics/2020/08/27/secant-mercator.html
+  * https://en.wikipedia.org/wiki/Fibonacci_sequence
+  * https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors