Category: Schwartz David M

What Is a Light Year?

10/18/2021

by David M. Schwartz
the amazing, engaging, math exponent

A light year is not a year that has gone on a diet. It is not a year that’s been trimmed to 300 days. It’s not a year spent under high-wattage lamps. A light year isn’t any kind of year.

    A light year is a distance. It is a vast distance; the distance light travels in a year. To appreciate a light year, you have to understand how fast light travels.

    The speed of light is truly mind-boggling: 186,000 miles per . . . second. That’s “per second,” not “per hour.” In one tick-tock second, light travels a distance of 186,000 miles. If it could go in circles, it could travel around the earth more than seven times in just one second! But light travels in straight lines, not in circles. Imagine something traveling that fast in a straight line—not for a second, not for a minute, not for an hour, not for a day, but for an entire year. The distance it goes in that year is called a light year.

    A light year is a convenient unit of measure when distances are enormous. You could talk about the same distances in miles. It's about 5,878,499,810,000 (5 trillion, 878 billion, 499 million, 810 thousand ) of them. But these measurements are so large that they are unwieldy. It's much easier to just name that enormous distance with two simple words: a "light year."

    The star closest to our solar system is Proxima Centauri. Some of the light that leaves Proxima Centauri goes to Earth, cruising along at 186,000 miles per second. At that speed, light takes about 4.2 years to get to Earth from Proxima Centauri So how far away is Proxima Centauri? It is 4.2 light years away.

    To give you an idea of how far that is, imagine going to Proxima Centauri in a spaceship traveling at the speed of the space shuttle — about ten miles per second. (That’s much faster than airplanes can fly.) You would get there in about 70,000 years.

    Our Sun is much closer than Proxima Centauri. It is 93 million miles away. There is another way to refer to the distance from the earth to the Sun. Light leaving the Sun takes about eight minutes to get to Earth, so we say the Sun is eight “light minutes” away. If you traveled at the speed of light, you could get there in eight minutes. Have a nice trip!

© David M. Schwartz, 2014

David Schwartz has been fascinated by big numbers and big distances ever since he was a little boy riding his bicycle, wondering “How long would it take for me to ride to Proxima Centauri, 4.2 light years away?” He wrote about light years in his math alphabet book G Is for Googol.

David is a member of iNK’s Authors on Call. He can visit in your classroom via interactive video conferencing. Learn more here.

MLA 8 Citation
Schwartz, David M. "What Is a Light Year?" Nonfiction Minute, iNK Think Tank, 14 Sept. 2017, www.nonfictionminute.org/the-nonfiction-minute/what-is-a-light-year.

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Happy Pi Day!

3/12/2021

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David M. Schwartz

The amazing,engaging, math exponent

Pi Day takes place on March 14th this year, as it has every year since 1988 when this mathematical holiday was invented. Pi Day? Does that sound crazy? Sure it does. It’s irrational. Pi is the world’s most famous “irrational” number. Therefore, Pi Day is the world’s most irrational holiday!

Take a circle, any circle, and divide the circumference by the diameter. The quotient is the number called pi, represented by the Greek letter π. It is a little more than three. How much more? That is a question that people have been working on for centuries.

Pi is an incredibly useful number in mathematics, physics and engineering. It helps us understand things from the shape of an apple to the energy of stars. It helps us design things, from buildings to spaceships.

Pi is an irrational number. That means when you write it as a decimal, its digits do not just end (like 3.5) and they do not repeat in a pattern (like 0.3333…, where the 3s go on forever).

Here is a slice of pi: 3.141592653… The “dot-dot-dot” means the digits keep on going. How far? Is there a pattern?

With supercomputers, mathematicians have probed the mysteries of pi to over a trillion digits. The digits keep going. Infinitely. No pattern has ever been found. (Written in an ordinary font, a trillion digits of pi would go around the world 50 times.)

But the endless, patternless nature of pi enchants many minds and some people delight in memorizing the digits. A 69 year-old man named Akira Haraguchi recited 100,000 digits from memory in Tokyo in 2006. He shattered the previous record of Chao Lu from China, who had memorized merely 67,890 digits of pi after studying for four years.

Can you see a date in the first three digits: 3.14? It’s March 14th — Pi Day! This holiday is celebrated worldwide by students, teachers and math enthusiasts who enjoy pi-themed activities, clothing, jokes and food (namely pie).

This is an ordinary year as far as Pi Day is concerned, but in 2015, Pi Day was really special. After 3.14, the next two digits of pi are 15. So March 14, 2015, was not just any old Pi Day. It was the “Pi Day of the Century.” You’ll have to wait until March 14, 2115, for another Pi Day so sweet!
Happy Pi Day, everybody!

The phrase on this T-shirt would be immediately understood by mathematicians. You won't learn about it for a few more years, but write it down and see if you can find someone who can read it

What better way to celebrate Pi Day than with a pi pie?

This chart shows many ways that pi can be formed -- just so you'll always recognize it when you see it. Pi is a mathematical symbol as well as a letter in the Greek alphabet. Can you find it in the alphabet chart? Hint: it follows Omega.

David Schwartz probes many mathematical mysteries in his books and school presentations given all over the world. He wrote this Nonfiction Minute while celebrating Pi Day at Tashkent International School in Uzbekistan. He is a member of iNK's Authors on Call and is available for classroom programs through Field Trip Zoom, a terrific technology that requires only a computer, wifi, and a webcam. Click here to find out more.

MLA 8 Citation
Schwartz, David M. "Happy Pi Day." Nonfiction Minute, iNK Think Tank, 14 Mar.
2018, www.nonfictionminute.org/the-nonfiction-minute/Happy-Pi-Day.

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If the Earth Were a Button

3/4/2021

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David M. Schwartz
The amazing, engaging, math exponent

Imagine Earth as a button. I don’t mean you’re going to sew it onto your shirt. But imagine the planet Earth shrunk to the size of a button. (Of course Earth is not flat like a button but we’re giving our shrunken Earth the same diameter as a shirt button.)

Go ahead and draw a circle around a shirt button. Call it “Earth.” Suppose you wanted to draw Jupiter, the largest planet, at the same scale as this micro-Earth. That means you’re going to shrink it to the same fraction of its original size as our button-Earth. What size would little Jupiter be?

One way to find out would be to calculate how many times bigger the real Jupiter is than the real Earth. Earth’s diameter is about 8,000 miles (13,000 kilometers). Jupiter’s is about 88,000 miles (143,000 km). Divide the size of Jupiter by the size of Earth to see that Jupiter is about 11 times bigger.

So, since Jupiter’s diameter is 11 times that of Earth’s, put 11 buttons in a line to show the diameter of Jupiter. Then draw the circle that represents Jupiter. If you don’t have 11 buttons, just look at the picture. Did you think the Earth was a big place? Look at it compared with Jupiter!

     But what about the sun? The sun’s diameter is about 865,000 miles (1,400,000 km). That means it’s almost 10 times bigger than Jupiter. Can you find a way to draw a circle 10 times the size of our Jupiter? We’ve drawn part of it for you, on the same scale as our button-sized Earth. On the picture, it’s labeled “our arc.” (An arc is part of a circle.) Looking at the arc, you can imagine the rest of the circle and compare the sun to Jupiter and Earth. A minute ago, you thought Jupiter was big. Now it looks shrimpy compared to the sun!

      But is the sun really gigantic? Do some research to find out the size of a red giant star like the strangely named Betelguese (pronounced “beetle-juice.”) Figure out what it looks like compared to our sun, which is a medium-sized star. You may be amazed at the difference. And you thought the sun was big!

      Is anything truly big? Is anything truly small? Or does that depend on what it’s being compared to?

If the Earth were the size of a button, Jupiter’s diameter would equal eleven buttons because the diameter of Jupiter is eleven times that of Earth.

Both images are by Marissa Moss, the illustrator of David M Schwartz's book, G is for Googol.

Extend “our arc” to complete the circle and you’ll see what the sun would look like if the Earth were the size of a button. (An arc is part of a circle.)

G is for Googol: A Math Alphabet Book is a wonder-filled romp through the world of mathematics.
For more information, click here.
David Schwartz is a member of iNK's Authors on Call and is available for classroom programs through Field Trip Zoom, a terrific technology that requires only a computer, wifi, and a webcam. Click here to find out more.

MLA Citation
Schwartz, David M. "If the Earth Were a Button." Nonfiction Minute, iNK Think
Tank, 16 Jan. 2018, www.nonfictionminute.org/the-nonfiction-minute/
If-the-Earth-Were-a-Button.

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Reading Has Gone to the Dogs

1/19/2021

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By David M. Schwartz
The Amazing, Engaging Math Exponent

A celebrity has just arrived in Mr. Madison’s classroom at El Verano Elementary School and the 3rd graders are beside themselves. “Here he is!” they exclaim as the visitor walks through the door.

This special guest has not come to give a lesson or tell a story. He is neither a star athlete nor a movie star. He doesn’t play an instrument, sing, dance or do magic tricks. His tricks are mostly limited to sit, stay and shake. He is a dog. His name is Fenway Bark.

An eight-year old chocolate-colored Labrador retriever, Fenway has been coming to El Verano for six years with his owner, Mara Kahn. He has helped hundreds of children become better readers. Fenway is a literacy dog.

“Fenway’s job is to listen while you’re reading,” explains Mara to the class, which is gathered in a circle around her and Fenway.

One of the best ways for children to improve their reading is to read aloud, but reading in front of an audience can be scary. What if Chelsea mispronounces a word? Or if Alex loses track of where he is on the page? Will everyone laugh? The fear can discourage some children from reading aloud at all.

Solution: read to a totally non-judgmental audience that doesn’t care what you read or how you read it. Read to a dog! When reading to dogs, young readers don’t have to worry about saying “whoof” when they meant to say “which.” With less anxiety and more confidence, young readers increase their reading fluency. That’s why literacy dogs visit hundreds of schools and libraries as reading buddies for children.

Vanessa sits cross-legged on the rug in Mr. Madison’s classroom. She gingerly opens Strega Nona by Tomie De Paola. Softly, slowly, she reads about Big Anthony who ignores Strega Nona’s instructions not to touch her magical pasta pot. Fenway sits up and looks at Vanessa. He gazes at the floor. Vanessa keeps reading. The pasta starts flowing. Fenway stretches out. Vanessa reads a little louder, a little faster. Pasta floods the town. Fenway licks Vanessa’s knee. She giggles and goes back to her book.

Today, six children got to read to the canine visitor. “It’s so cool to read to a dog,” said one boy who will get his chance next week. He was already thinking about choosing a doggone good book

Reading relaxes Fenway as well as the reader.

Animals as well as kids benefit from animal shelter reading sessions.

MLA 8 Citation
Schwartz, David M. "Reading Has Gone to the Dogs." Nonfiction Minute, iNK Think Tank, 20 Dec. 2017, www.nonfictionminute.org/the-nonfiction-minute/Reading-Has-Gone-to-the-Dogs. Accessed 20 Dec. 2017.

5 Comments

What's the Biggest Number?

12/3/2020

103 Comments

David M. Schwartz
The amazing, engaging, math exponent.

Can you put into words what these equations are telling you?

Think of a big number. How about one million? It's a thousand thousand. That's a lot. If you counted nonstop to a million, it would take you about 23 days.

A million is small compared to a billion, which is a thousand million. Want to count that high? You'll be at it for 95 years. But a trillion makes a billion look puny. A trillion is a thousand billion (or a million million). Counting that high would take you 200,000 years. Have fun!

Of course trillion is not the biggest number. There's quadrillion, quintillion, sextillion, septillion, octillion, nonillion, decillion and more. Each is a thousand of the previous one. There's even a humongous number called vigintillion, a one with 63 zeros.

But vigintillion is a shrimp compared to a googol. Googol? Notice how it's spelled: G-O-O-G-O-L, not G-O-O-G-L-E. The number googol is a one with a hundred zeros. It got its name from a nine-year old boy. A googol is more than all the hairs in the world. It's more than all the grass blades and all the grains of sand. It's even more than the number of atoms in the universe. Astrophysicists estimate the number of atoms to be a one with 82 zeros. You'd need to add 18 more zeros to get to a googol.

Incidentally, a few years ago, the two men who had invented a powerful new internet search engine decided to name their website and company for the gigantic number googol. But they spelled it wrong. That's why the company Google is spelled with an L-E. But the number googol is still spelled with an O-L.

Googol is so large that it's practically useless, but the boy who named it came up with a name for an even bigger number, "googolplex." A googolplex is a one with a googol zeros. There isn't enough ink in all the pens of the world to write that many zeros but feel free to give it a try.

So is googolplex is the biggest number? What about a googolplex and one? Two googolplex? A googolplex googolplex? Any number you say, I can say one bigger.

I hear you asking, "What about infinity? Isn't that the biggest number?" Sorry, but infinity isn't a number. A number specifies an amount and infinity is no amount. It means "goes on and on forever."

And that's what numbers do. They go on and on forever. Infinity is not a number but numbers are infinite.

Think you're too old for an alphabet book? You'll think again if you check out a sampling from David M. Schwartz's: B is for Binary, F is for Fibonacci, P is for Probability... You can see that this is an ABC book unlike any other. For more information, click here.

David Schwartz is a member of iNK's Authors on Call and is available for classroom programs through FieldTripZoom, a terrific technology that requires only a computer, wifi, and a webcam. Click here to find out more

MLA 8 Citation
Schwartz, David M. "What's the Biggest Number?" Nonfiction Minute, iNK Think Tank, 1 Dec. 2017, www.nonfictionminute.org/ Whats-the-Biggest-Number.

103 Comments

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What Is a Light Year?

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If the Earth Were a Button

Reading Has Gone to the Dogs

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