Monday, March 15, 2021

Lesson 12-8: The SSS Similarity Theorem (Day 128)

This is my annual post to mark the start of Daylight Saving Time. As usual, I will focus on current efforts to improve DST in this country. Recall the three choices for DST, in order of my preference:
  1. Year-Round DST
  2. Status Quo (i.e., biannual clock change)
  3. Year-Round Standard Time

But as we've discussed before, no state can unilaterally implement Year-Round DST. It takes an act of Congress to allow it. Of course, the focus of Congress right now is on the coronavirus and fixing all the problems associated with it -- and that's a little more important than Year-Round DST right now.

This week, Senator Marco Rubio of Florida reintroduced his Sunshine Protection Act -- a law that would bring Year-Round DST across our country:

https://www.brproud.com/news/u-s-senators-unveil-bill-to-make-daylight-saving-time-permanent-as-more-states-try-to-end-time-changes/

Of course, the bill isn't anywhere near passing the Senate yet. Thus we still had to move the clocks an hour forward this year. Then again, the change to DST is the one we want -- it's the change back to Standard Time that we're trying to eliminate. So we have until November to get the bill passed in order to make Year-Round DST official this year.

By the way, the following link discusses what's going on with California Proposition 7, which allows for Year-Round DST here:

https://www.capradio.org/articles/2021/03/14/daylight-saving-time-is-here-again-but-california-lawmakers-still-hope-to-get-rid-of-it/

In short, the state is now considering Year-Round Standard Time instead of Year-Round DST since, among other reasons, Congress isn't needed to implement it.

But as we see from my list of preferences, I'd rather keep the status quo than keep Standard Time. If there's to be a change to a single clock, it should be for Year-Round DST. Among other reasons, if California were to have Year-Round Standard Time and New England were to have Year-Round DST (as is being proposed there), we'd have an awkward four-hour time difference between the West and East Coasts.

One of the biggest advocates of Year-Round DST is Scott Yates:

https://www.sco.tt/time/

He states that his preference is to make Year-Round DST the default -- if a state does nothing, then they automatically get Year-Round DST. Only if a state prefers Year-Round Standard Time does it need to do something to opt out before DST becomes permanent.

As usual, here's some analysis of what's going on regarding DST choices around the world:

Nevada: A bill has been proposed for Year-Round DST in the Silver State:

https://www.ktnv.com/news/sb-153-aims-to-end-daylight-saving-time-in-nevada

I've suggested before that California shouldn't have Year-Round DST unless Nevada has it too -- otherwise we'd have a weird situation where the state to the west is one hour ahead of the the state to the east. Thus if California implements Proposition 7 time, Nevada should move forward too -- then California, Nevada, and Arizona would always have the same time.

Yukon Territory, Canada: Last year, Yukon implemented Year-Round DST. The clocks were set forward last March and they've remained forward since. (In fact, even before the change, it ought to be one hour behind Pacific Time based on its location but is in Pacific Time instead. Thus it observed the equivalent of Single Double DST, aka Lighter Later Time, before the change and Year-Round Double DST right now.)

One concern about Year-Round DST is that school starts in the dark in the winter, since sunrise is very late near the winter solstice. I looked it up, and found out that three months ago in December, the sun didn't rise in Yukon until around 11 AM! Then again, this meant that even under Standard Time, the sun rose around 10 AM on the winter solstice. The thinking behind Year-Round DST here is that the sun will rise after the start of school in winter no matter what, so we might as well have Year-Round DST so that there can be some light in the afternoon. Sunset is around 5 PM on the winter solstice -- around the same time that it sets here in Southern California.

A much more reasonable model for school schedules under Year-Round DST is in Saskatchewan -- a province that borders the U.S. yet doesn't change it clocks. (Based on its location, it ought to be in the Mountain Time Zone but it's in Central instead, so it observes the equivalent of Year-Round DST.)

It appears that in Saskatchewan, most schools start at 8:30 or 9 AM, which is around the time of sunrise in December and after sunrise in the other months. So northern states who are considering Year-Round DST but worried about starting school in the dark can follow the Saskatchewan school schedule.

Europe: The European Union was considering abolishing the biannual time change and letting its member nations choose either Year-Round Standard Time or Year-Round Summer Time (DST). But so far nations haven't chosen which clock they want, and so the clocks will still spring forward coming up on March 28th.

This is one reason why Scott Yates prefers simply implementing Year-Round DST and then having states opt out into Standard Time if they choose. If we leave it to states (or European countries) to choose a clock, then nothing ends up happening.

Morocco: This is an interesting case. Here in the U.S., we have DST for nearly eight months -- that is, it's actually the correct clock for almost two-thirds of the year. If I were to ask you which country has the longest period of DST without having Year-Round DST, the answer would be Morocco, which has DST for eleven out of twelve months.

And if I were to ask which one of the twelve months is the country still on Standard Time, the answer would Ramadan -- the Muslim month of fasting. This raises an important issue -- the relationship between Standard Time/DST and religious holidays, especially those that involve fasting.

Notice that the actual length of the fast doesn't depend on DST at all -- most religions specify that the fast should end at sunset, not any particular time on the clock. The only thing that DST determines is what you're doing (sleeping, working, going to school) when it's time to start and stop eating.

There are several differences between the Ramadan and the Jewish fasting holiday of Yom Kippur. First of all, the Yom Kippur fast lasts from sunset to sunset, so sunrise time is irrelevant. The Ramadan fasts, meanwhile, begin at sunrise and end at sunset. Also, Yom Kippur is a single day, while Ramadan is an entire month. Jews don't work on Yom Kippur, so the issue of whether Jews can make it home from work before the fast starts or ends is irrelevant. On the other hand, Muslims can't take a whole month off from work, and so they can and do work during the holy month, making the start and end times for the fast matter that much more.

And finally, Yom Kippur, as a lunisolar holiday, predictably occurs near the fall equinox, and so we know that sunset will be around 6 PM Standard Time or 7 PM DST. The Islamic calendar is purely lunar, and so we can't tie Ramadan to any season with a definite sunrise or sunset time.

Israel once considered springing forward after Passover and falling back before Yom Kippur. In many ways, this makes sense -- on the day before Yom Kippur, Jews eat early in the day so that they're not hungry at any time before bedtime, and on the holy day itself, sunset is around 6 PM and not 7 PM, so they're less hungry -- there's one fewer hour between waking up and sunset.

But to me, it's less clear whether Standard Time is better than DST for the Ramadan fast. I read that in recent years (with Ramadan falling near the summer solstice), the last meal before the fast (suhoor) was around 3:30 AM in Morocco, and the first meal after the fast (iftar) was around 8 PM. If the country were to have DST during the holy month, suhoor would be 4:30 and iftar would be around 9 PM.

I wouldn't want to wake up at 3:30 AM to do anything, including eat a meal. In fact, I wouldn't want to rise at 4:30 either, but 4:30 is "less bad" than 3:30. So the real question is, is being able to sleep until 4:30 worth having to wait until 9 PM for iftar instead of 8 PM?

As Ramadan approaches the winter solstice, suhoor and iftar both get closer to work hours. It would seem better to have iftar at 6 PM in winter, after getting home from work, than at 5 PM when still traveling from work. The relation between suhoor/iftar and school/bedtime hours is less relevant, since most children who, for example, have to go to bed before a 9 PM iftar in May are probably too young to participate fully in the fast anyway. (Only teenagers/adults are obligated to fast.)

But I'm neither a Moroccan nor a Muslim, so I have no right to tell Moroccan Muslims how to operate their clocks. Moroccan Muslims have made it clear that, while they like Year-Round DST, they prefer Standard Time during the fast. And so they've decided to set the clocks an hour back on the first of Ramadan and set it forward on Eid al-Fitr.

(Of course, if the desire is to shorten the actual fast, then Year-Round Standard Time doesn't do it. The only way to do that is to adopt a lunisolar calendar and make Ramadan the month that contains the winter solstice. But as I've written before in previous posts, leap months are forbidden in Islam.)

Returning to our country, the recommended time zones for Year-Round DST by longitude are:

125-110W: Pacific Forward Time
110-95W: Mountain Forward Time
95-80W: Central Forward Time
80-65W: Eastern Forward Time

Most people will set their clocks forward in March (of the year of implementation) and keep them there for their new time zone. A few on the far-western edges of time zones will opt out and keep clocks on Year-Round Standard Time (following the Scott Yates suggestion) to match these time zones.

Oh, and by the way, if we can't implement Year-Round DST, let's at least keep the day of the forward time change away from Pi Day. I didn't necessarily appreciate having Pi Day be one hour shorter than all the other days (even if it did lead to Vi Hart's video linking the time change and the math holiday).

Lesson 12-8 of the U of Chicago text is called "The SSS Similarity Theorem." In the modern Third Edition of the U of Chicago text, the SSS Similarity Theorem appears in Lesson 12-6.


This is what I wrote last year about today's lesson:

Let's get to our Geometry lesson. We are now working on the AA~ and SSS~ theorems, which complete our study of similarity. There are several ways we can prove these at this point. We can use the original dilation proofs given in the U of Chicago text (Lessons 12-8 and 12-9), or we can use the one similarity theorem we already have (SAS~) plus the corresponding congruence theorems (ASA and SSS, respectively). In the past, I reversed Lessons 12-8 and 12-9 but this year I'm preserving the original order, so no, we can't use SAS~ to prove SSS~.

I don't need to make any changes to last year's lesson. Last year, I created and posted a new instruction worksheet based on the U of Chicago method.

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