Archimedes and pi

 I've written a lot about Archimedes and the approximation of pi over the years (appropriated from the web, actually).

Most of that material is in my Analytic Geometry book.  I am in the process of re-doing the Github repos for the books, so they're not currently up-to-date, but that will change over the next week or so.  You can find me on Github here.

In the last couple of days, I wrote a summary of the math of Archimedes with respect to pi, including how his formulas connect with others based on perimeter and area that are due to Gregory.  There is also extensive discussion of methods to approximate the square root of 3, essential to Archimedes work.

That pdf is on Dropbox here.  Enjoy, and as always, comments would be welcome.

Pain with mac OS

I've run Macs ever since 1984.  Never had anything else except one Raspberry Pi running Linux.  

But I'm alarmed by clear signs of decay in QA for Mac system software.  Of course, they say you get what you pay for.  :)  But Apple is a hardware company and I've gladly paid a premium for a beautiful OS and well-designed hardware.

My current issue (though not the first) is the latest mac OS 11 (Big Sur).

So there I was, minding my own business, running Catalina and streaming video through the browser, Safari, when out of nowhere I got the spinning beachball.  Machine is unresponsive, unable to kill the app, transitioning to a black screen of death, which was new to me.  Bizarrely, it had a cursor which responded to the trackpad.

Luckily, there is this thing called googling.  Turns out you can press the power button for 10 seconds and the laptop will shut down.  Reboot and it seems fine.  So what happened?  The internet says that it has to do with system software updating, some conflict that happens with sleep.

I go to System Prefs > Software Update and it looks like this:

I never set this.  My 1 yr old laptop came with this as the default.  So the auto-updater crashes the machine.  Apparently it is downloading/installing Big Sur.

I uncheck everything.  Then, some demon tempted me to download and install Big Sur myself, which I did manually from the main screen for this preference.  Repeatedly (3x), I download 12 GB, the install fails, and then the 12 GB is deleted (or at least, neither I nor Update knows where it is).  You gotta start over.  The third time, I am on it when the download finishes, and I hit the button, so it goes.  

Not crazy about the updated UI, but that's life.

Now, one day later, there's an update.

Since auto-update can crash, I have only the first checkbox selected in the first window, above.  

I manually download the 11.1 update (Update Now).  Three times through, I download 3.x GB, then it stalls.  Right here.

 

I don't have the patience to do anything more.  I'm just angry.  How hard could it be to set up a fake install and test whether it works properly?  And then to throw it away each time.  They just don't frickin' care anymore.