Benjamin Leis @benleis@mathstodon.xyz

Anyone have advise for a friend's son who wants to study ap calc ab over the summer?

Mathjax is still not working anymore on the web version of my blogger hosted blog. So far I don't see error messages in the console

The college board has come out with the AP PreCalculus course. I haven't made my mind up (the details seem sketchy so far)

https://apcentral.collegeboard.org/courses/ap-precalculus/about-ap-precalculus

Mathjax works great

So we're ready to subsitute

\(p = \dfrac{p + q}{2} + \dfrac{p -q}{2} = \dfrac{-b}{2a} + \dfrac{\sqrt{ \left(\dfrac{-b}{a}\right)^2 - 4 \cdot \dfrac{c}{a}}}{2} \)

That simplifies to:

\( p = \dfrac{-b}{2a} + \dfrac{\sqrt{b^2 - 4ac}}{2a} \)

And the same goes for q.

\( a^2 + bx + c = 0 \)
From Vieta for the roots p,q: \(p +q = -\dfrac{b}{a} \text{ and } p\cdot q = \dfrac{c}{a} \)
Next each root root is symmetrically around the axis of symmetry through the vertex. Algebraically this is also easily verifiable.
\(p = \dfrac{p + q}{2} + \dfrac{p -q}{2} \)
We now just need an expression for p - q when we only have one for p + q

But

\( (p+q)^2 - 4pq = (p-q)^2 \)

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#potd - the image is a bit small the diagonal is of length 30 and the yellow square is of length 3

#potd - Find the ratio of the area of the red triangle to the green quadrilateral.

Also random notes

1. There doesn't seem to be way to find out how many times a toot has been seen (Even locally on this instance)

2. I don't understand how the forwarder bots on birdsite.wilde.cloud etal are setup. Can you get more accounts added?

3. Its a bit limiting not being able to search for terms to find things. No looking for other people who have discussed group theory unless they hashtagged it.

1st in the series. I've been collecting these for multiple years on https://blog.mathoffthegrid.com/p/collected-problems-2.html (and several followup pages)

#potd

Trying an experiment since I don't see many problems being posted - I'm going to do 1 a day from my back collection

Ah and I almost forgot I have a blog at blog.mathoffthegrid where I recently hosted one of the carnivals of Math but normally post about whatever mathy things I'm thinking about

One of the things I'm still looking for here is if anyone posts fun problems ala Catriona Agg etc,

A quick #introduction: I've been leading math circles mostly for middle school students the last five years,. So I'm always lookout for interesting activities or ideas to try out.

I host the local #mathsjam for Seattle. Recently we've been doing things virtually with the folks in Spokane and I've enjoyed getting to know the folks on that side of the state. Although I still very much miss in person get togethers and hope to do them again this summer.

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Also there seem to be some sort of bots now that can retoot things from twitter which I should look at

So I haven't really done anything with this account since I set it up 3 years ago. I'm still stuck with same problem of finding people and conversations since I'm back at square 1

Still don't quite have a handle on using mastadon. I just don't quite have the right circle of people to follow yet that makes it as interesting as twitter.

I need to figure out who to follow to get started.