I would like to get slightly more educated in mathematics again - I took some basic calculus and linear algebra classes while doing my degree, but most likely forgot what I learned for the most part. Are there any good books that you guys would recommend for someone who wants to learn math again?

While pondering an off-grid microcontroller project, I got to wondering: A light sensor can obviously detect day vs night. So it could be used as a very cheap way to set a device's clock - but how accurately? To within an hour? A few minutes? How would you do it?

Questions that arose from this include:

• Should it detect dawn/dusk (light <-> dark transition), or noon/midnight (brighest/darkest time) ?
• How do dawn/dusk times relate to clock time? Does it depend on lat/long?
• If using dawn/dusk, what light level threshold to use?
• The same threshold for dawn & dusk, or different ones?
• Better to detect a darker threshold (start of dawn, end of dusk) or a lighter one?
• Some days will be lighter/darker than others, so how to manage averaging of times?
• How accurate could it be made?

My naïve first stab at this would be: Pick a light threshold. Record the dawn/dusk times according to that threshold. Average them, call that "noon", and gradually tweak the clock time over several days to bring it into line with the sensed/calculated "noon" - but a searching for graphs of sunrise/sunset times quickly showed that the midpoint of sunrise & sunset is not noon.

Googling threw up lots of results for sensor lights combining a clock and a photocell, but I couldn't find anything about using the photocell to set the clock. So does anyone know if this has been tried before? Is it a non-starter for some reason?

Edit:

Perhaps it's worth sharing the project I had in mind, which is a rain alarm so I can rush out and get the washing in from the line when it starts to rain. I was thinking how annoying it would be if I left it switched on and it rained in the middle of the night and the alarm woke me up. So I decided should automatically avoid triggering during the sleeping hours of night (say 10pm to 8am). My first thought was a photocell so it wouldn't trigger when it's dark. Then I remembered that it gets light at 3am at the moment, which wouldn't work. So it needs a clock. How to set the clock:

• Manually - Needs a user interface with buttons and a display. Seems overkill just for a clock.
• Serial port - Clunky to plug a laptop in just to set the clock.
• WiFi - Needs a username and password or WPS, and an ESP32 or similar - again seems overkill just to get the time.
• GPS - also overkill and expensive.

So, I just listened to a This American Life podcast called Ghost in the Machine. In one of the stories, a man decides to calculate, every week, the Average Family Location of his family. By that, he means: once you add everyone's coordinates for every coordinate in which they've been in that period, what city/location represents the average point between them all?

I decided to do the same for my family, which will be much easier because there are no touring musicians among us. The one complication is that a good chunk of the family is on other continents, and I wouldn't want us to "meet" in the middle of the ocean. So some approximation might be warranted.

I'd be happy if someone could provide me the math, I'm fairly confident I would be able to do it with a calculator or maybe put into some crude Python. I don't think I need to make a weekly report, since we're not that mobile. Maybe twice a year, or once every two months.

Thanks!

Edit: I don't know much math

Edit2: holy shit this is not simple at all! Now I feel kinda bad for throwing this problem at you guys. I really thought it would be quick and easy!

So, my 5-year-old nephew is obsessed with huge numbers, especially named numbers such as googol, duodecillion, and centillion. The other day I spent some time reciting these numbers to him, and trying (and failing) to describe them. What I need are some cool facts about these numbers, such as "there are 1 quadrillion cat hairs in the world", or "there are not enough stars in the universe to fill one googol".

Besides math, his main interests are super-heroes and, apparently, cars.

I'm not a math or physics guy, so hopefully you guys can help me cheat :P