Chapter 8 Test (Day 121)

Today is a test day, and so as usual I'm labeling this post "traditionalists." The name Andrew Hacker has been in the news lately. He recently published a book arguing that students should not be forced to learn Algebra in order to graduate.

I could give a link to one of several different newspapers discussing Hacker's book and commenters who agree or disagree with Hacker. I chose the following link mainly because it is written by an actual mathematician -- Dr. Keith Devlin:

http://www.huffingtonpost.com/dr-keith-devlin/andrew-hacker-and-the-cas_b_9339554.html

I have much more to say about Hacker's side vs. Devlin's side of this issue, as well as my own opinion on which side is correct. But I will wait until next week to discuss this more. I'm waiting only because this weekend marks the start of Daylight Saving Time, when we spring forward one hour -- and so it's time for my biannual DST post. I can talk about Hacker at any time, but I pretty much have to discuss DST this weekend.

This is what I wrote last year about the time change:

For many people, "springing forward" is more difficult than "falling back." It's easier to get an extra hour of sleep than it is to lose an hour. Because of this, here's another DST proposal, by someone named Richard S. Holmes:

http://www.netfunny.com/rhf/jokes/90q2/dst.html

IMMODEST PROPOSAL #1: DAYLIGHT SAVINGS TIME REFORM
                              Richard S. Holmes
DAYLIGHT SAVINGS TIME

It happens every spring: crocuses, baseball, and the switch to Daylight Savings Time (DST).

Coming off DST is not hard. In the Fall, we set our clocks back one hour. We all get an extra hour to sleep, and those who forget find themselves at church, or the airport, or wherever an hour early. Embarrassing, but not catastrophic.

But in the Spring we set the clocks forward, and the trouble begins. We lose an hour of sleep. Forgetful people miss Mass, planes, breakfast, and the big game on TV. Some are thrown into disarray for up to a full week. Annual losses due to DST confusion have been estimated (by me) at over a million dollars. I myself have missed a flight to Washington and a showing of The Seven Samurai because of DST.

There is no need for such tragic waste. We can-we should and must- urge our lawmakers to reform Daylight Savings Time as follows: Setting clocks back is easy; setting them forward is difficult. Therefore, let us keep the fall ritual as it is. However, one Sunday each Spring, let us set our clocks not one hour forward, but TWENTY- THREE HOURS BACKWARD.

Think of all the advantages. We will not lose an hour of sleep; we will gain almost a day of rest. It will be Saturday all over again. You will never again miss Confession, or an airplane, or the Redskins game.

Naturally, if this were the whole plan, our calendars would fall behind one day in each year. However, the second part of the Revised DST Plan deals with this. Every four years, instead of adding a day, let us SUBTRACT THREE DAYS. Furthermore, let these be Monday, Tuesday, and Wednesday, which according to recent polls are the least popular days.

If done in February, which seems reasonable considering what a miserable month it is, this would have the beneficial side effect of shortening the excruciating presidential primary season by an effective four days.

The advantages of this plan are clear. Let us waste no time. With a determined effort we can have Reformed Daylight Savings Time by Spring of next year.

Write your congressperson today!
(By Richard S. Holmes)

This year, there is another real DST plan -- and it involves my home state of California:

http://www.refinery29.com/2016/03/105640/california-daylight-saving-time-bill

If you hate daylight saving time, you're not alone. 
Thanks to a proposed bill, it could soon go away entirely, at least for California residents. If the bill is passed and approved by voters, the state could join Hawaii and most of Arizona in choosing not to observe daylight saving time.

Here's my opinion of this bill -- there are actually two ways to abolish the biannual clock change. We could either have year-round standard time or year-round DST. It appears that Kansen Chu's bill will place California on year-round standard time.

Let's recall the original reason for the clock change in the first place -- it's to avoid having the sun rise too early or late during the year. The sun should rise close to the time that people wake up during the work or school week:

Ideal: sunrises between 6-7 AM

Tolerable: sunrises between 5-8 AM

Avoid: sunrises before 5 AM or after 8 AM

The closer one is to the poles, the clock change becomes more necessary. On the other hand, some states are far enough away from the poles that sunrises can remain within the tolerable range without needing to change the clocks. One such state is Arizona, which is why it doesn't observe DST.

Notice that Southern California borders Arizona, so we might be far enough south to avoid early and late sunrises without a clock change. Let's look at sunrise times at the solstices in Los Angeles, which I find using the following website, using standard time (ST) and daylight saving time (DST):

http://aa.usno.navy.mil/data/docs/RS_OneDay.php

Clock Change: 5:43 on June 21st, 6:55 on December 21st

Year-Round ST: 4:43 on June 21st, 6:55 on December 21st

Year-Round DST: 5:43 on June 21st, 7:55 on December 21st

Both year-round ST and year-round DST are good at keeping sunrise mostly between 5 and 8 AM, with DST slightly better at doing so.

This is one of several reasons that I prefer year-round DST to year-round ST for my hometown. I notice that year-round ST is often preferred by those with young children, as sunrise and sunset under ST are closer to the wake and bedtimes for children. But I don't have any young children, and so I, like many other adults, prefer year-round DST. But unfortunately, the Chu bill is for year-round ST, not year-round DST.

There are other reasons that I prefer year-round DST to year-round ST. Notice that year-round DST means that California and Arizona would have the same time all year. With year-round ST, the two states would always be an hour apart. Furthermore, the article means that New England is considering a year-round DST plan. If both the California and New England plans succeed, then the two regions would always be four hours apart rather than three.

If the idea behind abolishing DST is to simplify timekeeping, then the Sheila Danzig plan is best:

http://www.standardtime.com/

Under the Danzig plan, California would be on year-round DST while New England would be on year-round Standard Time. The two coasts would always be two hours apart, not four if both the Chu and New England bills past. (For simplicity, I'm going to refer to both the California and New England proposals as "the Chu plan," even though Chu has nothing to do with the New England proposals.)

Chu is from San Jose, which is farther north than Los Angeles. So let's see when the sun would rise in that city:

Clock Change: 5:48 on June 21st, 7:18 on December 21st
Year-Round ST: 4:48 on June 21st, 6:18 on December 21st
Year-Round DST: 5:48 on June 21st, 7:18 on December 21st


Here both plans are about equal -- year-round ST takes us 12 minutes outside the range, while DST takes us 18 minutes outside. So there will be a slight preference for Standard Time -- which is likely why Chu's bill is for year-round ST.


The biggest concern would be the far north, as in Eureka, CA:


Clock Change: 5:45 on June 21st, 7:38 on December 21st
Year-Round ST: 4:45 on June 21st, 7:38 on December 21st
Year-Round DST: 5:45 on June 21st, 8:38 on December 21st


With Eureka so far to the north, late winter sunrises are more of a problem. The sun doesn't rise until 8:38 under year-round DST, which is close to when tardy bells ring at elementary schools.


I also point out that if California switches to year-round DST, so should Nevada -- otherwise in the winter, we'd have to set our clocks back to go east. That is, both California and Nevada must collaborate to implement the Danzig plan, just as the New England states must work together to implement their proposal. Let's look at a town near the northern part of Nevada -- Elko:


Clock Change: 5:12 on June 21st, 7:04 on December 21st
Year-Round ST: 4:12 on June 21st, 7:04 on December 21st
Year-Round DST: 5:12 on June 21st, 8:04 on December 21st


For Elko, NV, year-round DST is clearly preferable to year-round ST -- the former takes us only four minutes outside the tolerable range, while the latter takes us 48 minutes outside.


For completion, let's look at one of the New England states. Here's the northernmost state, Maine -- I might as well take the capital, Augusta:


Clock Change: 4:55 on June 21st, 7:12 on December 21st
Year-Round ST: 3:55 on June 21st, 7:12 on December 21st
Year-Round DST: 4:55 on June 21st, 8:12 on December 21st


Here we see that year-round DST is clearly superior as it only takes us 17 minutes outside the tolerable range of 5 to 8 AM. Year-round ST has the sun rise more than an hour too early in the summer -- an hour of light that would be much better used in the evening.


So what is the best DST plan? It depends on what your overall goal is. For some people, changing the clock is so terrible that they'd have it dark at noon and light at midnight, if the only way to avoid either is to change the clock twice a year.


Of course, we can easily avoid noon darkness and midnight sun (except near the poles) without any biannual clock changes. Furthermore, we can keep sunrise mostly between 5 and 8 AM for much of the lower 48 states by adopting the Chu plan. This entails California adopting the assemblyman's plan of year-round ST and New England (and perhaps Nevada) adoping year-round DST.


This would result in a four-hour time difference between California and New England -- but according to those who hate the time change, anything (including a four-hour time difference between coasts) is better than a biannual clock shift. After all, the four-hour time difference would mostly matter to those who choose to travel between the coasts, but everyone is forced to change the clocks under the current DST status quo.


On the other hand, if simplifying the time zones is best, then the Danzig plan is preferable. With Danzig, the mainland U.S. has only two time zones, two hours apart. But we see that some northern locales have sunrises well outside the 5 to 8 AM range under Danzig (8:38 in winter in Eureka, 3:55 in summer in Augusta, ME).


And besides, those who hate the clock change might not mind Chu's four-hour time difference now, but just wait until the Olympics when it's time to complain about four-hour TV tape delays. Or for that matter, consider Monday Night Football when games begin at 5 PM Pacific Time when Californians are just leaving work, and ending at midnight Atlantic Time when New Englanders are already in bed.


I'm not sure how I'll vote on the bill. Most likely the bill won't appear on our ballots until 2018, so I still have a couple of years before I have to make a decision.


Let's worry about the Chapter 8 Test that I'm posting today on the blog. Here are the answers:

1. This is a triangle tessellation. The triangle is isosceles, so it shouldn't be too hard to tessellate.
2. One can find the area by drawing a square grid and estimating how many squares are taken up on the grid. Since the shape happens to be an ellipse, one can also find its area using the formula for the area of an ellipse -- pi * a * b, where a and b are the major and minor axes. That's right -- I had to slip in a reference to pi this week.
3. 5/2 or 2.5.
4. 12 square units.
5. 40 square units.
6. 6 mm. This is a trick if one forgets the 1/2 -- especially with 3-4-5 right triangles featuring in the last few questions, but here the legs are 6 and 4, not 3 and 4.
7. 10 feet.
8. 4.5s.
9. One can find the area by drawing a diagonal to triangulate the trapezoid. Then one adds up the area of the two triangles.
10. Answers may vary. The simplest such rectangle is long and skinny -- 1 foot by 49 feet.
11. Choice (a). The triangles have the same base and height, therefore the same area.
12. 3s^2.
13. 13 feet.
14. 6 minutes.
15. 780,000 square feet.
16. 133 square feet.
17. 1/4 or .25. Probability is a tricky topic -- the U of Chicago assumes that the students already know something about probability. Then again, it should be obvious that the smaller square is 1/4 of the larger square.
18. 4,000 square units.
19. 13.5 square units.
20. a(b - c) or ab - ac square units.