Documents for NATO

The lesson in class hopefully presented the necessary amount of information. In any case, here is the summary, and you can find the individual articles on the pages following.

[flash http://www.geekie.org/wp-content/uploads/2008/01/summary.swf h=715 w=552]

This is the only document that cannot be downloaded and saved to your computer as a PDF file.

Are you looking for the videos? Watch the CNN news clip at http://www.cnn.com/video/#/video/world/2008/01/02/oakley.uk.nato.year.ahead.cnn. The NATO video clip you saw can be found here.

This is page 1. The other articles can be found on subsequent pages. Click below to navigate.

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Documents for Midpoints and Midsegments

Our project between the three of us (Frederick, Davin, Adam) was “midsegment conjectures for triangles and parallelograms”.

What we’ve demonstrated (hopefully), is that:

• The length of any midsegment in a triangle is equal to half of the side to which it is parallel
• The inscribed polygon of any triangle has an area that is a quarter the area of the triangle
• The inscribed polygon of any parallelogram is half the area of the parallelogram
• The perimeter of the inscribed polygon in any parallelogram is equal to half of the sum of the diagonals

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Back from Montreal

Now that I’m finally back from Montreal, I’ll be posting a few photos from our trip to McGill University for their debate tournament.

This is just a short post with little purpose.

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Branded merchandise for corporate events

I was recently made aware of a site called “Gimmees” that offers a number of promotional items such as badges, T-shirts, mugs, magnets, keychains, and more.

You might know that I am a member (supposedly an executive member) of RASA, also known as the Space Club. RASA is planning on fundraising sometime within the next little while. Interestingly, Gimmees offers some of the things that can help us raise cash.

RASA could do one of the following things:

• Order custom badges, and distribute them to club members; sell badges to students;
• Order custom pens/pencils, and sell them at a price CHEAPER than the “little shop in the wall”, thus encouraging competition for the monopoly that the “little shop” is;
• Order frisbees with the logo, and sell them for profitable prices;

There are all sorts of things that we could do with the products offered by this business. Might I add that Gimmees offers a lot of things that you don’t find elsewhere?

Interestingly, this sponsor offered something that I could actually benefit from buying, unlike some of Geekie.org’s previous advertisers. I am being honest when I say that I will try to promote Gimmees over the course of a few months, as well as increase its awareness within our fundraising operations at RASA. It’s one of the first times that I’ve found an advertiser that I would buy from.

Unfortunately, some of the minimum purchase quantities make it a bit less feasible for RASA to buy — Student Council / the school Administration are unlikely to approve a $250+ purchase for 200 frisbees. It’s not the individual unit prices driving the cost up — those are quite good — but rather the setup prices.

Fortunately, Gimmees’ prices (including setup costs) are lower than their competitors, and we will give some thought to this provider. Larger companies, school-approved events, will have no problems getting what they want at a suitable price from Gimmees.

Now, if you’re a student at Richmond Hill High School, be sure not to leak out the low, low prices that Gimmees offers; a few weeks from now, you might see us selling them at largely inflated prices!

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The earth is round

When was the last time a reputable person challenged the common consensus that the Earth is spherical? Additionally, when was the last time someone called a curved arc a “straight line”?

Why is a high school teacher telling students that lines of latitude and longitude are “straight”?

These are matters that should not be of much controversy in these days of science and technology. We know that the Earth is round, and that the world around us is in at least 4 dimensions.

We do not say that the surface of the Earth is flat. Neither do we accept that lines of latitude and longitude are “straight”.

It is common knowledge that a string wrapped around an orange does not represent a straight line. Likewise, lines of latitude and longitude — despite their respective differences — are NOT straight. Although they are determined based on the Earth as a large body, we must never forget that we are in a world where the first 3 dimensions are crucial.

Thinking in a three-dimensional manner, latitudinal lines extend 90 degrees south of the equator and 90 degrees north. Because the Earth is roughly spherical — not cylindrical — no adjacent lines of latitude are equal in circumference. Furthermore, as the Earth is NOT flat as an infinitely thin plane, these lines curve downwards (from a human perspective). Thus, lines of latitude on the surface of the globe, although parallel, are neither congruent nor straight.

Similarly, lines of longitude also curve due to the spherical nature of the Earth. To say that curved lines are straight is a huge violation of mathematics. Parallel Walking at Newton - Ask a Scientist, states:

“Lines” of latitude are not straight lines in this geometry, however, but rather curved arcs. So you can make no conclusions about people walking along them. They are not straight because a straight line, or geodesic, is always defined as that path defining the shortest distance between two points. On the surface of a sphere that kind of line is always a great circle…

…You can see that all lines of longitude are great circles…

I do not claim to be a mathematician, but it is taught to children in elementary school that curves are not straight lines. How can any geographer — especially one involved in the instruction of a course at Richmond Hill High School — claim, that:

• lines of latitude are straight and parallel
• lines of longitude are straight and meeting ???

The Pennsylvania Department of Conservation and Natural Resources has a classroom map activity for students between the grades of 4 and 6. Really — kids in elementary school are learning these facts –

Find the latitude lines on the map and lay the ruler along them. The students SHOULD find these lines are NOT STRAIGHT and cannot be drawn with a ruler. Discuss why this occurs, peel the orange and flatten the peel to demonstrate why latitude lines are curved.

A different site, with the article A world globe as a reference tool, clearly explains:

Just about everyone knows the old rule: The shortest distance between two points is a straight line. But if you look at a flat map of the world, the paths followed by airplanes and ships are not straight lines. They look like curves. That is because the world is round, not flat. The shortest distance between two points on the globe is a “great circle route.”

For children, this is a simple explanation that gets the point across — although it does not go as far as to say that the true shortest distance between two points on the globe is through the mass that we know as our planet. In any case, it makes clear that any “straight” line on the surface of the globe is really a curve.

Before I stop attacking those that say that lines of latitude and longitude are “straight”, I must acknowledge the following:

Lines of latitude and longitude, when drawn on reasonable and accurate projections of the globe on paper, are usually not straight. However, in the simplest of ways, it is possible to consider them straight — but only in 2D.

As if I haven’t said this enough already, as soon as the third dimension comes into play, we realize that any line across the surface of the Earth is really a curve.

The definition of meridian clearly illustrates this principle:

A meridian (or line of longitude) is an imaginary arc on the Earth’s surface…

NOTE: when it is an arc, it is NOT straight.

How many people out there can honestly state that:

1. The Earth is flat or otherwise non-spherical;
2. Lines of latitude and longitude are not curves, but straight lines, and;
3. Everything being taught to children in schools today is entirely false?

If you can, leave a comment. If not, leave one anyways.

I rest my case.

The lines of latitude and longitude are not straight, since they are on the surface of a sphere. -The Digital Library at the University of Chicago

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