Pythagoras for Kids

July 21, 2011 · Posted in Math · Comment 

 

Pythagoras

http://www.historyforkids.org/learn/greeks/science/math/pythagoras.htm

Pythagoras lived in the 500s BC, and was one of the first Greek mathematical thinkers. He spent most of his life in the Greek colonies in Sicily and southern Italy. He had a group of followers (like the later disciples of Jesus) who followed him around and taught other people what he had taught them. The Pythagoreans were known for their pure lives (they didn’t eatbeans, for example, because they thought beans were not pure enough). They wore their hair long, and wore only simple clothing, and went barefoot. Both men and women were Pythagoreans.

Pythagoreans were interested in philosophy, but especially in music and mathematics, two ways of making order out of chaos. Music is noise that makes sense, and mathematics is rules for how the world works.

Pythagoras himself is best known for proving that the Pythagorean Theorem was true. The Sumerians, two thousand years earlier, already knew that it was generally true, and they used it in their measurements, but Pythagoras is said to have proved that it would always be true. We don’t really know whether it was Pythagoras that proved it, because there’s no evidence for it until the time ofEuclid, but that’s the tradition. Some people think that the proof must have been written around the time of Euclid, instead.

Here is the proof:

The Pythagorean Theorem says that in a right triangle, the sum of the squares of the two right-angle sides will always be the same as the square of the hypotenuse (the long side). A2 + B2 = C2. Try it yourself: if Side A is 4 inches long, and Side B is 3 inches long, then 4×4=16, and 3×3=9, and 9+16=25, and so Side C will be 5 inches long. Try it with other size triangles and see if this is still true (you can use a calculator, or your computer, to figure out the square roots).

But how can you know that this is always true, every single time, no matter what size the triangle is?

Take a straight line and divide it into two pieces, and call one piece a and the other piece b, like this:

Now make a square with this line on each side, like this:

and draw in the lines where A meets B on each side to make four smaller shapes. So now you have one square with area AxA (the big yellow one) and one square with area BxB (the little green one) and two rectangles with area AxB (the light blue ones). So the area of the whole square is (A+B) x (A+B) or the area is (AxA) + 2(AxB) + (BxB).

Or you might say that
(A+B)2 = A2 + 2AB + B2

Now draw diagonal lines across the blue rectangles, making four smaller blue triangles. Call those lines C. Do you see that you have made four blue right triangles, whose sides are A, B, and C?

Now imagine that you take these triangles and rearrange them (or if you print it out you can cut them up with scissors and really rearrange them) around the edges of the square like this:

The little triangles take up part of the square. The area of all four triangles together is the same as the two blue rectangles you made them from, so that is 2AB.

The area of the pink square in the middle is CxC or C2.

And the area of the whole big square is, as we have already seen,
A2 + 2AB + B2
So A2 + 2AB + B2 = 2AB + C2
We can subtract 2AB from both sides, so
that gives (ta da!)

A2 + B2 = C2

Here’s an animated short video showing another way to prove the Pythagorean Theorem.

Tsunami hits Alexandria, Egypt Jul 21, 365

July 21, 2011 · Posted in Uncategorized · Comment 
Tsunami hits Alexandria, Egypt. (2011). The History Channel website. Retrieved 3:47, July 21, 2011, from http://www.history.com/this-day-in-history/tsunami-hits-alexandria-egypt.
Alexandria Egypt
On this day in the year 365, a powerful earthquake off the coast of Greece causes a tsunami that devastates the city of Alexandria, Egypt. Although there were no measuring tools at the time, scientists now estimate that the quake was actually two tremors in succession, the largest of which is thought to have had a magnitude of 8.0.

The quake was centered near the plate boundary called the Hellenic Arc and quickly sent a wall of water across the Mediterranean Sea toward the Egyptian coast. Ships in the harbor at Alexandria were overturned as the water near the coast receded suddenly. Reports indicate that many people rushed out to loot the hapless ships. The tsunami wave then rushed in and carried the ships over the sea walls, landing many on top of buildings. In Alexandria, approximately 5,000 people lost their lives and 50,000 homes were destoyed.

The surrounding villages and towns suffered even greater destruction. Many were virtually wiped off the map. Outside the city, 45,000 people were killed. In addition, the inundation of saltwater rendered farmland useless for years to come. Evidence indicates that the area’s shoreline was permanently changed by the disaster. Slowly, but steadily, the buildings of Alexandria’s Royal Quarter were overtaken by the sea following the tsunami. It was not until 1995 that archaeologists discovered the ruins of the old city off the coast of present-day Alexandria.

Today, the anniversary of the tsunami is celebrated annually with the residents saying prayers and marking the evening by illuminating the city.

The First Battle of Bull Run

July 21, 2011 · Posted in Uncategorized · Comment 
Jul 21, 1861:
Battle of Bull Run--July 21st 1861-500

The First Battle of Bull Run. (2011). The History Channel website. Retrieved 3:20, July 21, 2011, from http://www.history.com/this-day-in-history/the-first-battle-of-bull-run.

In the first major land battle of the Civil War, a large Union force under General Irvin McDowell is routed by a Confederate army under General Pierre G.T. Beauregard.

Three months after the Civil War erupted at Fort Sumter, Union military command still believed that the Confederacy could be crushed quickly and with little loss of life. In July, this overconfidence led to a premature offensive into northern Virginia by General McDowell. Searching out the Confederate forces, McDowell led 34,000 troops–mostly inexperienced and poorly trained militiamen–toward the railroad junction of Manassas, located just 30 miles from Washington, D.C. Alerted to the Union advance, General Beauregard massed some 20,000 troops there and was soon joined by General Joseph Johnston, who brought some 9,000 more troops by railroad.

On the morning of July 21, hearing of the proximity of the two opposing forces, hundreds of civilians–men, women, and children–turned out to watch the first major battle of the Civil War. The fighting commenced with three Union divisions crossing the Bull Run stream, and the Confederate flank was driven back to Henry House Hill. However, at this strategic location, Beauregard had fashioned a strong defensive line anchored by a brigade of Virginia infantry under General Thomas J. Jackson. Firing from a concealed slope, Jackson’s men repulsed a series of Federal charges, winning Jackson his famous nickname “Stonewall.”

Meanwhile, Confederate cavalry under J.E.B. Stuart captured the Union artillery, and Beauregard ordered a counterattack on the exposed Union right flank. The rebels came charging down the hill, yelling furiously, and McDowell’s line was broken, forcing his troops in a hasty retreat across Bull Run. The retreat soon became an unorganized flight, and supplies littered the road back to Washington. Union forces endured a loss of 3,000 men killed, wounded, or missing in action while the Confederates suffered 2,000 casualties. The scale of this bloodshed horrified not only the frightened spectators at Bull Run but also the U.S. government in Washington, which was faced with an uncertain military strategy in quelling the “Southern insurrection.”

Atlantis comes in for its final landing

July 21, 2011 · Posted in Uncategorized · Comment 
Posted at 08:41 AM ET, 07/21/2011

Video

By 


(Bill Ingalls/AP)


Just before sunrise, the space shuttle Atlantis made its final landing, putting to bed the 30-year U.S. shuttle program. “Like a UFO in the dark, fiery contrails lighting Florida up,” Beth Carpenter wrote on Twitterin one of the many elegies.

The NASA Goddard Photo and Video team put together a short, sweet tribute to the last flights of Discovery and Atlantis. In the first few seconds, Discovery moves past the night side of the Earth into the daytime, as the Aurora Borealis clings to Earth’s side. In the second, the Discovery shuttle moves over a cloudy United States. And in the last few moments, the sun rises behind Atlantis in this time-lapse sequence on July 19, 2011, just two days before it landed:

(Watch the video here)

 

By Melissa Bell  |  08:41 AM ET, 07/21/2011

http://www.washingtonpost.com/blogs/blogpost/post/atlantis-comes-in-for-its-final-landing-video/2011/07/21/gIQAwJVcRI_blog.html

Sinking was disaster but ship was engineering triumph

July 18, 2011 · Posted in Uncategorized · Comment 
30 May 2011 Last updated at 21:31 ET

Mark SimpsonBy Mark Simpson BBC Ireland Correspondent

titanic launch

The Titanic is no longer a taboo topic in Belfast as the city marks 100 years since the luxury liner’s launch.

Back in April 1912, there was a sense of embarrassment when the “unsinkable” ship hit an iceberg and went under.

Fast forward a century and Belfast is no longer hiding from its Titanic past.

The launch, maiden voyage and sinking of the ship will all be marked in the city which now boasts its own Titanic Quarter, full of residential and commercial ventures including a tourist trail.

“What happened to Titanic was a disaster but she was not,” says Una Reilly, co-founder of the Belfast Titanic Society.

“It’s amazing to think that we here, in this small corner of the then empire, made the biggest ship in the world.”

“We have an awful lot to be proud of. We are not very good at blowing our own trumpets, but we are re-claiming that pride.”

It was on 31 May 1911 that Titanic, held together by three million rivets, first entered the water.

Even though the famous four funnels were not yet in place, and none of the ornate furnishings had been completed, it was still quite a sight as the huge vessel entered Belfast Lough.

Crowds gathered to watch the launch, but the spectacle did not last long.

The Rev Chris Bennett, who helps conduct Titanic walking tours, says it took just over a minute for the ship to slide from land to sea – thanks to the appliance of industrial quantities of soap, grease and oil.

“The command was shouted to ‘release the triggers’ and it took just 62 seconds. A massive wall of riveted metal came scraping and screaming down the slipway into the sea,” he said.

At the time, it was largest man-made moving object on earth. The floating hotel was built by Harland and Wolff whose workforce in 1911 was around 15,000-strong.

One of the deck engineers, Thomas Millar, not only helped to build the ship, but sailed on her doomed maiden voyage from Southampton to New York. He was one of the 1,517 passengers and crew who died when she sank.

His great grand-daughter, Susan, now runs Titanic tours and has written a book about Thomas Millar.

“Belfast kept quiet about its Titanic connection for too long,” she says.

“We can now start to share that story with the rest of the world. For so long, we didn’t know how to deal with Titanic. We were a bit embarrassed about it, but now we have come to a place where we can celebrate it as an achievement.

“It was a beautiful ship and a beautiful piece of engineering.”

Although the shipyard in east Belfast gained a reputation in the 20th Century as a bastion of Protestant unionism, recent research has shown that Catholics were also involved in the three-year construction project.

Una Reilly says: “The workforce was mixed. There were actually thousands of Catholics employed at the time. Of course, things changed afterwards, but at the time the Titanic was built by all of us.”

She says Belfast was the “Cape Canaveral” of shipbuilding, with the very latest technology used to build the Titanic.

The problem was that no ship was unsinkable, and the fact that Titanic hit the iceberg side-on meant more of the vessel was damaged as she scraped along the iceberg than might have been the case in a head-on collision.

The Titanic did have a number of water-tight compartments – but not enough. The ship also had a chronic shortage of lifeboats for such an emergency.

A ship designed to accommodate 3,511 passengers and crew only had lifeboat capacity for 1,178 people. To make matters worse, some lifeboats were launched before being totally filled.

Nonetheless, there is no doubting that the ship was a remarkable feat of early 20th Century engineering.

When Belfast people are asked about the Titanic, they often remark “she was all right when she left us”.

As the decades have passed since the disaster, the blame game over the Titanic has turned into a tourist trail.

Fuelled by the 1997 blockbuster movie Titanic, people from across the world have traced the ship’s final movements from Belfast to Southampton to the Atlantic seabed, two miles below the surface.

Indeed, as the centenary of the sinking on 14 April 1912 approaches, the Titanic movie stars Kate Winslet and Leonardo DiCaprio are likely to be invited to take part in the anniversary events.

An invitation from Belfast is in the post already.

Follow Mark Simpson on Twitter: @BBCMarkSimpson


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