Lesson 1-2: Locations as Points (Day 12)

This is what Theoni Pappas writes on page 243 of her Magic of Mathematics -- a table of contents for Chapter 10, "Mathematics & Architecture":

-- Buckminster Fuller, Geodesic Domes & the Buckyball
-- 21st Century Architecture -- Spacefilling Solids
-- The Arch -- Curvy Mathematics
-- Architecture & Hyperbolic Paraboloids
-- The Destruction of the Box & Frank Lloyd Wright

And so these are the topics we'll be discussing in Pappas throughout the next two weeks as we discover the link between math and architecture.

Lesson 1-2 of the U of Chicago text is called "Locations as Points." (It appears as Lesson 1-1 in the modern edition of the text.) The main focus of the lesson is graphing points on a number line. Indeed, we have another description of a point:

Second Description of a Point:
A point is an exact location.

Yesterday I made a big deal about the first description of a point -- the dot -- since many of our students are interested in pixel-based technology. Locations as points aren't as exciting -- but still, the second description is something we think about every time we find a distance. The definition of distance is highlighted in the text:

Definition:
The distance between two points on a coordinatized line is the absolute value of the difference of their coordinates.

Other than this, the lesson is straightforward. Students learn about zero- through three-dimensional figures, but of course the emphasis is on one dimension. One of the two "exploration questions," which I included as a bonus, is:

-- Physicists sometimes speak of space-time. How many dimensions does space-time have?

Hey, we were just discussing this in Pappas! The answer, of course, is four -- even though there might be as many as ten dimensions in string theory. We ordinarily only include Einstein's four dimensions and don't consider the extra six dimensions of string theory as part of "space-time."

Here's the other bonus question:

-- To the nearest 100 miles, how far do you live from each of the following cities?
a. New York
b. Los Angeles
c. Honolulu
d. Moscow

Well, part b is easy -- I worked in L.A. last year and my daily commute obviously wasn't anywhere near 100 miles, so my distance to L.A. is 0 miles to the nearest 100 miles. The U of Chicago text gives the distance from L.A. to New York as 2451 miles as the crow flies, but 2786 miles by car. I choose to give the air distance in part a, in order to be consistent with parts c and d (for which only air distance is available). We round it up to 2500 miles. My answers are:

a. 2500 miles
b. 0 miles
c. 2600 miles
d. 6100 miles

Hmmm, that's interesting -- I'm only slightly closer to New York than to Honolulu.

Today is the last day of August -- hence the last day of Blaugust. I don't consider any of my posts to be Blaugust posts, since I'm not currently a teacher.

The most dedicated Blaugust poster is Illinois high school teacher Jackie Stone. She made an amazing 26 posts during the month. And as she's a Geometry teacher, it's interesting to compare her posts to what I write about on this blog.

https://mathedjax.wordpress.com/2017/08/25/my-favorite-five-minute-games-blaugust/

In this post, Stone begins:

Today I gave pre-assessments in all of my classes.  It is a necessary evil in this world of data driven decisions.

And of course, I posted Benchmark Tests earlier this week. But Stone's post isn't actually about the pre-assessments, but about quick activities to do when there are five minutes left in class. (Last year, my activity for the last five minutes of class was called "Exit Pass.")

Of course, just because Stone is from Chicago, it doesn't mean that she uses the U of Chicago text -- or, for that matter, the Illinois State text.