Reading Comprehension

1.Read the following text about the Origins of Mathematics.

Tallies and Tablets - The Origins of Mathematics
By Colleen Messina

1     Have you ever wondered what a teraflop is? No, it is not a clumsy, prehistoric fish. A teraflop is a unit that measures the speed of computer calculations. One teraflop is 1 trillion calculations per second, and today there are computers that can sustain speeds of 35.86 teraflops! These incredible electronic calculations originated with the idea of numbers and counting. Most of us take math for granted, but numbers and counting have taken thousands of years to develop. So how did it all begin?

2     Tens of thousands of years ago, our ancestors found their food by hunting for meat and gathering wild plants. Survival was a constant struggle. Little did they realize that some mathematics could vastly improve their lives. For example, if they knew when certain berries were ripe, they could save themselves a lot of wandering time by only going to the berry thickets at precisely the right moment. The hunters and gatherers of ancient times needed something constant in their environment to help them track time.

3     The most constant thing in their world was the sky since the landscape changed through the seasons of the year. Early peoples observed the geometry in nature, the cycles of the seasons, and the splendor of the Milky Way. Our ancestors noticed the moon's pattern of becoming full, then slender, then full again in a recurring thirty-day cycle. This cycle gave them a key to solving the dilemma of tracking time. With this knowledge, they observed that sour, green berries took approximately a full cycle of the moon to ripen, so they began to cut notches in a tree or a stick to keep track of the days of the lunar cycle. Harvesting the berries and other food became much more efficient with this new system.

4     The idea of keeping track of the lunar cycle sounds simple, but it was a momentous event in the evolution of mathematics. Our ancestors were keeping a tally, for the first time, and they probably began to use this form of counting in other areas of their lives. The earliest known tallies were carvings in bones dated approximately 15,000 years ago, which were discovered in the area now known as the Middle East. Putting pebbles or shells in a pile was another way of keeping a tally. Keeping track of items by using simple marks or objects was still a long way off from the invention of numerals, but it was a big step forward.

5     Another way that early people kept track of things was by using "body counting." Different parts of the body represented different amounts of things. For many thousands of years people counted using their ten fingers, and some tribes took this idea even further. The Paiela tribe, who lived in the highlands of Papua New Guinea, counted by pointing to different parts of their bodies to represent different numbers. For example, their little fingers represented the number "one." Other fingers, wrists, elbows, shoulders, ears and eyes all represented different numbers up to twenty. Body counting worked fine as long as there was no need for large numbers.

6     When our ancestors became farmers, they needed to keep track of larger amounts of things. Farming probably started when the hunters and gatherers visited a campsite where they had lived during the previous season and noticed grain growing from seeds they had accidentally dropped on the ground. They learned to save seeds and sow crops rather than gather wild plants. They also learned to keep sheep, goats, and cows in pens and slaughter them rather than hunt for wild animals. Life became easier, and villages formed since no one had to wander around to survive. A better system of counting evolved because the men who became shepherds had to count their animals, and the men who became farmers had to keep track of their harvest.

2. Answer the following questions.

What is a teraflop?
  A unit of measurement for computer calculations
  The missing link in man's evolution
  A clumsy, prehistoric fish
  An archaeological artifact
What does the word, "lunar," mean in paragraph 3?
Which of the following is not a fact from the article?
  Tallies began about 15,000 years ago
  A lunar cycle is 6 months long
  A written system of numbers was developed about 5000 years ago (3000 B.C.)
  Sometimes pebbles were used to keep a tally
How long is a lunar cycle?
  30 days
  3 days
  Thousands of years
  The article does not say
Where were the earliest known devices for keeping tallies found?
  The Middle East
  North America
  South America
Where did the Sumerians live?
South America
What is missing in the Sumerian system of numbers?
What is a quipas?
  An ancient joke
  An ancient numeral
  A knot in a cord used for counting
  An ancient game

3. Read the following text about the Age of Discovery.

The Age of Discovery - Gravity and Gauss
By Colleen Messina

1     By the seventeenth century, mathematics had come a long way from the tallies and abacuses of the ancient world. Mathematicians had finally adopted the new Arabic numbers, as well as the symbols for addition, subtraction, multiplication, and division. Logarithms made difficult problems much easier, and calculus opened up new possibilities in science. Mathematicians applied these new tools in exciting ways ranging from world exploration to astronomy. Ships crisscrossed the oceans to new places, and telescopes scanned the skies and discovered the elliptical orbits of planets. The understanding of gravity revolutionized military science. It was truly an age of discovery.

2     The discovery of gravity especially changed how people viewed the world. Up until the 16th century, people thought that heavy objects fell faster. A feisty Italian named Galileo Galilei had another idea. In 1585, he climbed to the top of the leaning Tower of Pisa, made sure no one was down below, and dropped two objects. One object was heavy and the other was light, but both reached the ground at the same time. Galileo proved that objects fall at the same rate and accelerate as they fall. Eventually, military engineers understood that a cannonball shoots out in a straight path, but the force of gravity makes the cannonball fall downward in a curve called a parabola. The engineers could then fortify their strongholds in the right places, and artillerymen could shoot their cannons more accurately. Galileo's experiment revolutionized military science.

3     Galileo also did experiments with pendulums that helped clockmakers design accurate clocks. Seamen needed accurate time-keeping devices to navigate during long journeys. The weight-driven clocks of the previous centuries were not accurate enough; now seamen needed to measure minutes and seconds, so the new clocks were invaluable. Navigators then accurately plotted the daily positions of their ships on maps that had vertical and horizontal lines of latitude and longitude. When they connected the dots on these grids, they saw an accurate record of the ship's journey.

4     Rene Descartes, a great French mathematician and philosopher, also liked grids. He had a big nose and a sheath of black hair that came down to his eyebrows. He always stayed in bed until late in the morning and said that that was the only way to get ready to do mathematics! Descartes tied geometry and algebra together by writing equations for a geometric shape, like a parabola, on a graph. His analytic geometry became the foundation of the higher mathematics of today, and some people call him the first modern mathematician. The Cartesian coordinate system is named after Descartes.

5     Another mathematician who laid the foundation for higher math was a number-crunching prodigy. In 1779, three-year-old Carl Friedrich Gauss watched his father add up the payroll for a crew of bricklayers and pointed out a mistake his father made in the calculations! When Gauss was 14, a wealthy Duke noticed his incredible abilities and was so impressed that he sponsored Gauss's entire education. This patronage was well deserved, as Gauss dominated mathematics of the nineteenth century.

6     Gauss first became famous when an Italian astronomer discovered an asteroid in 1801. Joseph Piazzi accidentally found a minor planet and then lost sight of it in the bright sky near the sun. This new planet, called Ceres, caused a great rush of excitement all over Europe. When it disappeared, astronomers were upset because they didn't know how to find the new planet again. Gauss used the tables of logarithms he had memorized to predict where Ceres would reappear. The tiny planet showed up on the other side of the sun just where Gauss said it would! Gauss received many honors from scientific societies because of this triumph.

4. Answer the following questions.
Which scientist performed an experiment from the top of the Tower of Pisa?
What field was affected by Galileo's experiments with gravity?
  Counting machines
  Military science
Check which discoveries Galileo made from the Tower of Pisa experiment.
  Objects accelerate as they fall.
  Objects fall at the same rate regardless of weight.
  A scientist should warn people before dropping objects from great heights.
  The Tower leaned too much to make the experiment useful.
What kind of geometry did Descartes develop?
Why did Carl Gauss first become famous?
  He located a lost asteroid.
  A wealthy duke financed his education.
  He loved complicated equations.
  He was brilliant at an early age.
What is unique about a complex number?
  It involves negative numbers.
  It involves the square root of minus one.
  It is very large.
  It is used in complicated equations.
What was John Napier's counting machine called?
  Napier's bones
  Napier's multiplier
  Napier's calculator
  Napier's abacus
Who was the first computer programmer?
Albert Einstein
  John Napier
  Charles Babbage
  Ada Lovelace

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