445: Early Hard Drives

This 1961-era 1MB hard drive is too small to hold this picture.

This 28MB IBM 1301 machine cost $110,000 and weighed half a ton.

And now you have this to carry around in your pocket.

Go here:
http://www.jcmit.com/flashprice.htm

Can you compose a simple rule about prices over time?

Data copied here:

X	Y	Year	Month	Sales Company	Manufacturer	Size	Size	Cost
date	US$/MB						MBytes	US$
2003.17	0.258	2003	25-Mar	NewEgg.com	Samsung	128MB Flash	128	33
2003.58	0.191	2003	19-Aug	NewEgg.com	Dana-Elec	256MB Flash	256	49
2003.75	0.219	2003	1-Oct	NewEgg.com	Delkin	256MB Flash	256	56
2004	0.191	2004	Jan	pcclub.com	Simpletech	256MB Flash	256	49
2004.17	0.238	2004	16-Mar	NewEgg.com	SanDisk	256MB Flash	256	61
2004.33	0.266	2004	4-May	NewEgg.com	SanDisk	256MB Flash	256	68
2004.42	0.223	2004	8-Jun	NewEgg.com	SanDisk	256MB Flash	256	57
2005.5	0.0762	2005	July	Crucial.com	Crucial	512MB Flash	512	38.99
2006.33	0.0219	2006	25-May	NewEgg.com	Transcend	2GB Flash	2048	43.98
2006.67	0.0156	2006	1-Sep	NewEgg.com	Patriot	4GB Flash	4096	63.99
2006.83	0.0146	2006	25-Nov	NewEgg.com	PNY	2GB Flash	2048	29.98
2007	0.0122	2007	28-Jan	NewEgg.com	Wintec	4GB Flash	4096	49.98
2007.17	0.0104	2007	15-Mar	NewEgg.com	Transcend	8GB Flash	8192	84.98
2007.33	0.0105	2007	7-May	NewEgg.com	Kingston	2GB Flash	2048	21.58
2007.5	0.00976	2007	9-Jul	NewEgg.com	R-Data	4GB Flash	4096	39.98
2007.67	0.00805	2007	30-Sep	NewEgg.com	A-Data	4GB Flash	4096	32.98
2007.75	0.00763	2007	16-Oct	NewEgg.com	A-Data	16GB Flash	16384	124.98
2007.83	0.00732	2007	10-Nov	NewEgg.com	Corsair	8GB Flash	4096	29.99
2007.92	0.00763	2007	5-Dec	NewEgg.com	Corsair	16GB Flash	16384	124.99
2008	0.00458	2008	18-Jan	NewEgg.com	A-Data	16GB Flash	16384	74.98
2008.08	0.00463	2008	20-Feb	NewEgg.com	PQi	4GB Flash	4096	18.98
2008.33	0.00415	2008	18-May	NewEgg.com	A-Data	16GB Flash	16384	67.98
2008.5	0.00354	2008	7-Jul	NewEgg.com	A-Data	16GB Flash	16384	57.98
2008.58	0.00305	2008	21-Aug	NewEgg.com	A-Data	16GB Flash	16384	49.98
2008.67	0.00311	2008	25-Sep	NewEgg.com	Transcend	16GB Flash	16384	50.98
2008.83	0.00183	2008	14-Nov	NewEgg.com	A-Data	16GB Flash	32768	59.99
2008.92	0.00214	2008	14-Dec	NewEgg.com	Corsair	32GB Flash	32768	69.99
2009	0.00162	2009	19-Jan	NewEgg.com	OCZ	16GB Flash	16384	26.49
2009.08	0.00168	2009	14-Feb	NewEgg.com	HP	8GB Flash	8192	13.75
2009.25	0.00204	2009	3-Apr	NewEgg.com	Patriot	64GB Flash	65536	133.99
2009.42	0.00214	2009	3-Jun	NewEgg.com	A-Data	16GB Flash	16384	34.99
2009.5	0.00195	2009	2-Jul	NewEgg.com	A-Data	16GB Flash	16384	31.99
2009.58	0.00177	2009	20-Aug	NewEgg.com	A-Data	32GB Flash	32768	57.99
2009.75	0.00214	2009	7-Oct	NewEgg.com	Corsair	16GB Flash	16384	34.99
2009.92	0.00226	2009	12-Dec	NewEgg.com	A-Data	16GB Flash	16384	36.99
2010	0.00244	2010	15-Jan	NewEgg.com	Corsair	32GB Flash	32768	79.99
2010.08	0.00226	2010	11-Feb	NewEgg.com	Lexar	16GB Flash	16384	36.99
2010.17	0.00244	2010	10-Mar	NewEgg.com	HP	8GB Flash	8192	19.99
2010.33	0.00201	2010	9-May	NewEgg.com	PNY	16GB Flash	16384	32.99
2010.5	0.00193	2010	25-Jul	NewEgg.com	Kingston	8GB Flash	8192	15.85
2010.58	0.00176	2010	26-Aug	NewEgg.com	Lexar	16GB Flash	16384	28.85
2010.75	0.00177	2010	7-Oct	NewEgg.com	Kingston	16GB Flash	16384	28.99
2010.83	0.00146	2010	16-Nov	NewEgg.com	OCZ	16GB Flash	16384	23.99
2010.92	0.00119	2010	10-Dec	NewEgg.com	Patriot	32GB Flash	32768	38.99
2011	0.001403	2011	21-Jan	NewEgg.com	Transcend	16GB Flash	16384	22.99
2011.08	0.001251	2011	12-Feb	NewEgg.com	Verbatim	32GB Flash	32768	40.98
2011.33	0.001342	2011	6-May	NewEgg.com	Patriot	16GB Flash	16384	21.99
2011.42	0.001219	2011	22-Jun	NewEgg.com	Transcend	16GB Flash	16384	19.98
2011.67	0.001007	2011	2-Sep	NewEgg.com	Team	32GB Flash	32768	32.99
2011.75	0.001037	2011	17-Oct	NewEgg.com	Verbatim	16GB Flash	16384	16.99
2012	0.000824	2012	12-Jan	NewEgg.com	Corsair	32GB Flash	32768	26.99
2012.08	0.000824	2012	13-Feb	NewEgg.com	Team	32GB Flash	32768	26.99
2012.25	0.000793	2012	8-Apr	NewEgg.com	Team	32GB Flash	32768	25.99
2012.33	0.000702	2012	24-May	NewEgg.com	HP	32GB Flash	32768	22.99
2012.58	0.00058	2012	20-Aug	NewEgg.com	Transcend	32GB Flash	32768	18.99
2012.62	0.00061	2012	21-Sep	NewEgg.com	Kingston	16GB Flash	16384	9.99
2012.83	0.00061	2012	17-Nov	NewEgg.com	Kingston	16GB Flash	16384	9.99
2013	0.000458	2013	17-Jan	NewEgg.com	DNY	64GB Flash	65536	26.99
2013.08	0.000518	2013	23-Feb	NewEgg.com	Lexar	32GB Flash	32768	16.99
2013.33	0.00058	2013	18-May	NewEgg.com	Transcend	64GB Flash	65536	37.98
2013.42	0.000564	2013	30-Jun	NewEgg.com	Transcend	64GB Flash	65536	36.98
2013.58	0.000564	2013	9-Aug	NewEgg.com	Transcend	64GB Flash	65536	36.98
2013.62	0.000564	2013	7-Sep	NewEgg.com	Transcend	64GB Flash	65536	36.98
2013.75	0.000534	2013	16-Oct	NewEgg.com	Centon	64GB Flash	65536	34.98
2013.83	0.000542	2013	10-Nov	NewEgg.com	Centon	128GB Flash	131072	70.98
2013.92	0.000548	2013	23-Dec	NewEgg.com	AData	16GB Flash	16384	8.98
2014.08	0.000457	2014	8-Feb	NewEgg.com	Transcend	32GB Flash	32768	14.98
2014.17	0.000473	2014	13-Mar	NewEgg.com	Team	64GB Flash	65536	30.98
2014.25	0.000366	2014	10-Apr	NewEgg.com	Silicon Power	32GB Flash	32768	11.99
2014.42	0.000389	2014	19-Jun	NewEgg.com	PNY	128GB	131072	50.98
2014.58	0.000335	2014	2-Aug	NewEgg.com	Adata	32GB Flash	32768	10.98
2014.67	0.000345	2014	13-Sep	NewEgg.com	Silicon Power	64GB Flash	65536	22.58

191: Walking the Labyrinth

In this labyrinth, there are no false turns or dead ends. You walk the line around the outside, then follow it to the middle. Assume unit distance between lines and ends of turns except for that horizontal entry line. That seems to be half a unit apart from the other lines.

What are some different ways to measure the distance walked?

155: Pre-Medieval Math, Pyramids part two

Here are the pyramids at Giza, viewed from a satellite. Notice that they are aligned to the north-south lines ... in fact, to within a 0.05 degree. Also measurements of the plateau they sit on have determined that the foundation was carved into the bedrock and the entire site was leveled to within a fraction of an inch.

It's known how the Egyptians managed to perform this feat with the simple tools they had ready and now it's time for you to consider it and try to figure it out..

String, standard measuring sticks carved from granite, a good pair of eyes, that's all. Remember, they were just as smart as you and you are just as smart as they.

1. How did they align the edge N-S?
2. How did they level the base so precisely? 

Give up? Look at the alt text of the photo.

Was it aliens?

No, that's just crazy talk.

Look at the alt text for the pyramid photo for the explanation.

Here's another ..

154: Pre-Medieval Math, Pyramids

From Bryn, O.J. 2010. Retracing Khufu’s Great Pyramid, Nordic Journal of Architectural Research vol. 22, no 1/2, 135-144. 

You must enlarge this to see the detail.

Interpret the construction layout, Find the angle of the sides .... heck, you know how this works.

153: More Manuscript Geometry

Straightedge, compass and a pencil ... GO.

152: Medieval Geometric Constructions

Ok, you have a straightedge and a compass, and a steel point to scribe with.
Geometrical constructions ....

GO.

Symmetry.

Images are of the Alhambra, of course.

151: Medieval Altitude Measurement

Explain the reasoning used in 1588 to find the height of the castle.

So they could shoot it.

150: Angle of Elevation in 1588

If that inclinometer says 40° between the cannon's mouth and plumb, what's the angle of elevation?

149: Medieval Ballistics

Tartaglia

Using the angle between line of sight to the projectile and the horizontal, show why the trajectory was considered to be in this shape for many centuries. (Hint: consider that only those viewing from BEHIND could see the projectile. UPDATE: Yes, those in front could see something coming. "I couldn't figure out what it was coming closer and closer ... then it hit me.")

This may be more than you want ... if so, pay no attention to the following instructions.

In Geogebra, graph the parabolic arc. We'll assume for simplicity that the cannonball begins at (0,0) and hits at (1000,0) with max at (500,250). In the input box, place y=x(x-1000)/1000. Place A at (-10,0) and B, a point on the object f(x). Place c(500,0) so we have three points. Create line segments AB and AC. Measure CAB. Drag B along the curve, paying attention to the angle.  What do you see?
How does it change as you move B?

148: Medieval Math - Polyhedra

From manuscript dated 1585,
Houghton Library. MS Typ 108. Geometrica et Perspectiva Corpora Regulata et irregulata.

Q9: Imaginary Numbers

Question 9: Why were imaginary numbers invented?

113: The Address

How long would it take everyone in your school to recite it?

272 words (or 269, depending on how you count, and which version you use.)

On November 19th Lincoln traveled to Gettysburg to dedicate the new Union Cemetery

The featured speaker was Edward Everett of Massachusetts, a diplomat, clergyman, and celebrated orator. The president had been invited almost as an afterthought to offer a few appropriate remarks. Everett spoke for not quite two hours.

Then Lincoln rose. The local photographer took his time focusing; presumably the president could be counted on to go on for a while ... but he spoke just 269 words.

He started off by reminding his audience that just 87 years had passed since the founding of the nation and then he went on to embolden the Union cause with some of the most enduring words ever spoken.

Lincoln was heading back to his seat before the photographer could open the shutter.

He felt that he had failed, that it was a poor speech, that people didn't like it. It was so brief, less than two minutes, he felt that he had failed. His friend, Ward Lehman, was sitting next to him on the stand when he sat down and there was just a sprinkling of applause.

He said "Lehman, that speech won't scour." That's what you say about the plow in the prairies when the mud won't come off it."

"The cheek of every American must tingle with shame when he reads the flat, silly, dish watery utterances of the man who has to be pointed out to intelligent foreigners as the president of the united states."  Chicago Sun-Times

"Dear Mister President, I should be glad if I could flatter myself that I came as near to the central idea of the occasion in two hours as you did in two minutes." - Edward Everett

President Lincoln delivered the 272 word Gettysburg Address on November 19, 1863 on the battlefield near Gettysburg, Pennsylvania.

"Fourscore and seven years ago our fathers brought forth, on this continent, a new nation, conceived in liberty, and dedicated to the proposition that all men are created equal. Now we are engaged in a great civil war, testing whether that nation, or any nation so conceived, and so dedicated, can long endure. We are met on a great battle-field of that war. We have come to dedicate a portion of that field, as a final resting-place for those who here gave their lives, that that nation might live. It is altogether fitting and proper that we should do this. But, in a larger sense, we cannot dedicate, we cannot consecrate—we cannot hallow—this ground. The brave men, living and dead, who struggled here, have consecrated it far above our poor power to add or detract. The world will little note, nor long remember what we say here, but it can never forget what they did here. It is for us the living, rather, to be dedicated here to the unfinished work which they who fought here have thus far so nobly advanced. It is rather for us to be here dedicated to the great task remaining before us—that from these honored dead we take increased devotion to that cause for which they here gave the last full measure of devotion—that we here highly resolve that these dead shall not have died in vain—that this nation, under God, shall have a new birth of freedom, and that government of the people, by the people, for the people, shall not perish from the earth."

6: Why 360?

Everyone knows that there are 360 degrees in a circle.

We can also take it as a given that people who did math back in the days of Babylon didn't mess around ... they must have had really good reasons for choosing that number.  They were logical and just as smart as we are now, even if we sometimes don't admit that.

How many good reasons can you think of for 360° in a circle?
How many ridiculous reasons can you think of for 360° in a circle?

Should we change to another number for doohickeys in a circle?