typo fix in hourglass; new draft for pi

_drafts/approximating-pi.md

@@ -0,0 +1,14 @@
+---
+layout: post
+title:  "Approximating π"
+tags: math calculus
+katex: True
+---
+
+A fun thing to do at the end of a Calculus II class is to use Taylor series to compute values of various functions. For instance, I have a whole problem set about the "68-95-99.7" rule, where we find a Taylor series for the normal distribution and then integrate it. Here's another fun application:
+
+## Approximating $\pi$
+
+"Everybody" knows that $\pi \approx 3.14$. Some people know considerably more digits off the top of their head. (You should probably be suspicious of those people.) But how do we actually know what those digits are? When you ask your computer or calculator what π is, how does it know? There are lots of approaches to this question (some more efficient than others) but here's one that's fun and accessible to students in a Calculus 2 course.
+
+When I start thinking about π, I start thinking about radians.

_posts/2024-04-18-hourglass.md

@@ -12,7 +12,7 @@ If I ask you what shape an hourglass is, there is a very specific shape that lea
 
 For Physics Reasons (TM), fluids[^1] will flow more quickly out of a more full container than they will out of an emptier container, so if we want the level of the fluid to drop consistently, we need the sides to taper in to compensate. 
 
-Exactly how much taper do we need? WHat shape, in fact, is an hourglass? Turns out this is a fun question to explore with just a little calculus.
+Exactly how much taper do we need? What shape, in fact, is an hourglass? Turns out this is a fun question to explore with just a little calculus.
 
 ## Solids of revolution