Category: Mathematics

What's the Biggest Number?

3/13/2023

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.

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The Science Behind the Olympics

2/24/2023

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Jennifer Swanson
Shining the Spotlight on Science and Technology

When you think of the Olympics you think of the sports: Speed skating, Bobsled. Snowboarding. Track, Gymnastics. Swimming. Tennis. Just to name a few.

You may even think about some of the Olympians: Snowboarders Shaun White and Kelly Clark. Speed skater Apollo Ohno. Swimmers Michael Phelps and Katie Ledecky. Or even gymnast Simone Biles and sprinter Usain Bolt.

But do you ever think about the science behind each sport? You should. Math and physics play a huge part in every part in the Olympics. Think about it. One of the most basic forces, friction, is a factor in everything an athlete does. What is friction? It’s the force that pushes back on you as you swim through the water or run through the air. Friction not only affects an athlete, but also the object they may be throwing, hitting, or kicking—like a baseball, a tennis ball, or a soccer ball.

Movement of any kind deals with physics of air flow, engineering design, and (unfortunately) sometimes collision. The verdict? Athletes need to know a LOT of science to do well in their sports.

Science is not just found in the activities themselves but also in the equipment they use and clothes they wear. Most of today’s superstar athletes rely on clothing and equipment enhanced with nanotechnology. What is nanotechnology? Nanotechnology is the science of the super small—microscopic even. One nanowire is 1,000 time thinner than a single strand of human hair. Now that is SMALL! Materials made with nanotechnology are stronger, more durable, and yet lighter and more flexible.

Nanotechnology produces swimsuits that allow the athlete to glide through the water faster, golf clubs that hit the ball farther, and tennis rackets that flex more easily to provide the hard smash across the net. This innovative new technology has already been used in the Olympics. In 2008, swimmers Michael Phelps and Natalie Coughlin wore swimsuits that were created with nanofibers. These nanofibers are woven tightly so that the swimmer’s bodies become more streamlined (like a shark!) allowing them to glide through the water faster. In the 2014 winter Olympics, the U.S. speed skaters wore specially created vented suits (like the swimsuits—to reduce drag), and in the 2018 winter Olympics, the USA Snowboarders will be wearing snow gear inspired by the space program.

Nanotechnology is a cutting-edge science that is changing the world of sports—and in particular the Olympics— as we know it. Will you make nanotechnology part of your game?

The LZR Racer is a line of completion swimsuits manufactured by Speedo using a high-technology swimwear fabric. In March 2008, athletes wearing the LZR Racer broke 13 swimming world records. Much like other suits used for high competition racing, LZR Racers allow for better oxygen flow to the muscles, and hold the body in a more hydrodynamic position, while repelling water and increasing flexibility. Kathy Barnstorff via Wikimedia Commons

Serena Williams uses a nanotech racket and Phil Mickelson uses nanotech technology in his game. Seems to be going well for both of them. (l) Wikimedia Commons (R) Photo by Siyi Chen via Wikimedia Commons

A graphic highlighting all of the ways nanotechnology enhances the effectiveness of sports equipment. Nanowerk via Wikimedia

You would have to increase a carbon nanotube x100,000 to make it the size of a strand of hair.
NIEH.gov

Want to know more? Jennifer Swanson's Super Gear: Nanotechnology and Sports Team Up was listed as one of the 2016 Best STEM Books by the National Science Teachers Association.
Colorfully illustrated by photos, this book introduces "the science of the very small" as applied to sports equipment and clothing.

MLA 8 Citation
Swanson, Jennifer. "The Science Behind the Olympics." Nonfiction Minute, iNK
Think Tank, 7 Feb. 2018, www.nonfictionminute.org/the-nonfiction-minute/
the-science-behind-the-olympics.

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The Great Boston Molasses Flood: How Can a Tragedy Sound Funny?

2/6/2023

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Jan Adkins
The Explainer General

Most disasters are a cascade: small failures and minor circumstances, one leading to another, blossom into a cataclysm. On January 16, 1919, a cascade of tremendous size was poised above Boston’s North End.

The weather was one factor: unusually warm for winter.

Purity Distilling Company fermented and distilled molasses to make rum and alcohol. The 18th Amendment to the United States Constitution, prohibiting sales of alcoholic beverages, was due to be passed the very next day. This may have prompted Purity to collect as much molasses as possible.

The enormous tank holding the molasses was about 50 feet tall and 90 feet in diameter, holding 2,300,000 gallons. It was poorly built of thin steel painted brown to hide its leaks. Local families often collected some of the dripping molasses to sweeten their food. The unseasonably warm temperature quickly rose from 2° F (-16.7° C) to 40° F (4.4° C), expanding the liquid, and natural fermentation produced CO2 increasing tank pressure.

Just after noon, North End families felt the ground shake and heard a sound like a machine gun— the tank’s rivets popping out. The big tank exploded, sending a 25-foot wall of molasses roaring down the hill toward Commercial Street at about 35 miles an hour. In front of the molasses went a blast of air that blew some folks off their porches and tumbled others along the street like rag dolls. Homes and buildings were destroyed, smashed from their foundations. Horses pulling wagons were swept away. The steel girders of the Boston Elevated Railway were buckled, knocking a rail-car off the tracks.

Twenty-one people were killed and more than a hundred were injured. Many were saved by Massachusetts Maritime Academy cadets who rushed off their docked training vessel and plunged into the brown goo to rescue people. It’s difficult to know how many dogs, cats and horses died.

As you can imagine, the clean-up was awful. Firehoses from hydrants and harbor fireboats washed away as much as possible. Boston Harbor was brown for months. Sightseers tracked the goo back to homes, into hotels, onto pay-phones and onto doorknobs. Everything Bostonians touched was sticky for months.

Some say that on a hot summer day along the North End’s docks, the sickly sweet smell of molasses lingers. Bostonians can smile at the Great Molasses Flood now, but in January of 1919, that cascade of disasters was deadly serious.

Aftermath of the disaster; photo by Globe Newspaper Co. (Boston Public Library)

Damage to the Boston Elevated Railway due to the flood

Coverage from The Boston Post

Jan Adkins is an author, an illustrator, and a superb storyteller. Read about him on his Amazon page. He is also 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
Adkins, Jan. "The Great Boston Molasses Flood: How Can a Tragedy Sound Funny?"
     Nonfiction Minute, iNK Think Tank, 19 Jan. 2018,
     www.nonfictionminute.org/the-nonfiction-minute/
     The-Great-Boston-Molasses-Flood-How-Can-a-Tragedy-Sound-Funny?

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How Old Are You—in Seconds?

4/8/2022

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David M. Schwartz
The amazing, engaging, math exponent

Do you want to be a lot older? Here’s how: state your age in seconds instead of years!

Ready to do some math? But what math will you do?

First you have to design a problem-solving strategy. There are many approaches but for all of them, consider that with every passing second, you are a second older. So your age is a moving target. Best to pick a specific time of day and find your age in seconds at that time today.

It doesn’t really matter what time of day you pick. If you can find out from your birth certificate what time of day you were born, you could select that time today for your target. If you were born at 4:14pm, you will find out how old you are (in seconds) at 4:14pm today.

Or just pick any time today and pretend you were born at that time.

What next? I hope you will try out your own approach but here is a simple strategy that would work:

Step 1. How many days old are you? Figure out how many days elapsed between the day you were born and your most recent birthday. There are 365 days in a year, not counting leap years. In your lifetime, every year divisible by 4 was a leap year and it had a 366th day, which was February 29th. So add an extra day for each February 29th you’ve lived through.

Then figure out how many days have passed since your last birthday. Try to find a way to make this job quicker than counting each day. Look at calendars as you do this to find shortcuts.

Now you have your age in days. It’s already looking like a big number, isn’t it? Just wait!

Step 2. How many seconds are in a day? Think about how to figure this out. You know how many seconds are in a minute (60) and how many minutes are in an hour (60) and how many hours are in a day (24). So how many seconds are in a day? Multiply 60 X 60 X 24. Bet you didn’t realize a day was so long!

Step 3 So what’s Step 3? You now know how many days you have lived and how many seconds are in a day, so what do you do next? Again, multiply!

Next time someone tells you you’re not old enough to do something, you can tell him or her, “Oh yes I am. I’m 299,592,620. That’s what I was at 11:30 this morning. Now I’m even older!”

Good luck with that!

A is for “abacus,” B is for “binary,” C is for “cubit”
and W is for “When are we ever gonna use
this stuff, anyway?” David M. Schwartz's G is for Googol: A Math Alphabet Book is a wonder-filled romp through the world of mathematics. For more information, click here.

David 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.

Schwartz, David. "How Old Are You...in Seconds?" Nonfiction Minute, iNK Think
Tank, 3 May 2018, www.nonfictionminute.org/the-nonfiction-minute/
How-Old-Are-You-in-Seconds.

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Isaac Newton's Wonder Years

3/28/2022

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Kerrie Logan Hollihan
Teaching the Power of Wonder

   In spring 1665 a college student named Isaac Newton studied natural philosophy, what we call “science.” Back then, a good student could learn everything to know about the natural world. But plague, the Black Death, came to England. Cambridge University closed. Isaac went home to Woolsthorpe.

            For two years Isaac thought about his studies during four years at university. He’d always been thoughtful—not the best at games, making friends, or minding sheep. But everybody knew Isaac Newton liked to think. Folks told time by the sundial he’d drawn on a wall.

            Home at Woolsthorpe, Isaac’s learning about science and math bubbled up in his head like yeast rising in a loaf of bread.

            So... Newton unplugged. His mind roamed like that of an artist or composer. He was driven by the need to create—not paintings or symphonies, but questions.

            “Why do things always fall down?”

            “Why does the earth move around the sun?

            “Why doesn’t the moon fall onto the earth?”

            “Does everything ‘up there” work like things work ‘down here?’”

            Isaac Newton answered his questions with three science rules, Newton’s Laws of Motion.

            At Woolsthorpe, Newton grappled with the concept of moving objects. He worked out the math to find the area under curves. He called this math fluxions. Today we call this calculus, useful for launching rockets or tracking TV signals.

            Once back at Cambridge, Newton said nothing until he read someone else’s paper on fluxions. Newton published a better paper. Soon he was Cambridge’s top math professor.

            Isaac Newton wondered another twenty years. He played with prisms in a dark room and theorized that white light comprises the visible spectrum of red, orange, yellow, green, blue, indigo, and violet. He practiced alchemy and chemistry, looking for the legendary philosopher’s stone to turn base metals to gold. In 1687, Newton published our most important science book, the Principia.

            In the Principia, Newton showed how laws of gravity and motion work the same at great distances—far off in space, or in your classroom. We accept these ideas, but in 1687 many still had medieval beliefs that sun, moon, planets, and stars all traveled in their own crystal spheres.

            Yes, Newton wondered about A LOT:

Gravity
Forces
Mass
Inertia
Math
Motion
Light
God
???

Whatever interests you, I hope you’ll think about it—a lot! Like Isaac Newton, take time to WONDER!

Sir Isaac Newton was an English mathematician, astronomer, theologian, author and physicist who is widely recognized as one of the most influential scientists of all time and a key figure in the scientific revolution. Based on a portrait by Godfrey Kneller, 1702, via Wikimedia Commons

Sir Isaac Newton's own first edition copy of his Philosophiae Naturalis Principia Mathematica with his handwritten corrections for the twentieth edition. Photograph Andrew Dunn via Wikimedia Commons

Trinity College, the part of the University of Cambridge where Newton worked and lived. Library of Congress

This statue of the young Isaac Newton stands at the Oxford University Museum of Natural History. Look carefully around his feet for a hint on what he is wondering about. If you can’t figure it out, then read about Newton and gravity.
Wikimedia Commons

Featuring 21 hands-on projects that explore the scientific concepts Isaac Newton developed, Kerrie Logan Hollihan's Isaac Newton and Physics for Kids paints a rich portrait of the brilliant and complex man and provides readers with a hands-on understanding of astronomy, physics, and mathematics. A time line, excerpts from Newton's own writings, online resources, and a reading list enhance this unique activity book.

MLA 8 Citation
Hollihan, Kerrie Logan. "Isaac Newton's Wonder Years." Nonfiction Minute, iNK
Think Tank, 21 Feb. 2018, www.nonfictionminute.org/the-nonfiction-minute/
isaac-newtons-wonder years.

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What's the Biggest Number?

The Science Behind the Olympics

The Great Boston Molasses Flood: How Can a Tragedy Sound Funny?

How Old Are You—in Seconds?

Isaac Newton's Wonder Years

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