Category: Schwartz David M

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.

274 Comments

Rot Rocks!

10/31/2022

2 Comments

David M. Schwartz
The amazing, engaging, math exponent

'Tis the season. The rotting season.

You thought Halloween was full of ghosts, goblins and ghouls? Well, wait until the post-Halloween season. This is when your Jack O' Lantern begins its ghoulish decline. It starts as a pumpkin and it ends as a heap of goo. This is scary!

Now is when your Halloween pumpkin begins to rot. Don't get me wrong. Rot is not gross. It is a beautiful thing—beautiful in its own deliciously disgusting way.

You start with a proud Jack, a plump, shiny-skinned pumpkin. Halloween is over so you leave it on your porch, or inside by the window, or maybe you toss it into the garden or onto the compost heap.

It attracts some visitors. A squirrel. A pair of mice. A scurry of sow bugs. They chew the skin of the pumpkin, leaving moist, rough surfaces, just perfect for the next wave of invaders: the molds and fungi and bacteria that start to grow. There are dozens, even hundreds, of types of organisms waiting to sink their "teeth" into pumpkin flesh as soon as the conditions are right. One kind of invader changes the conditions of the flesh to make it perfect for the next one. Meanwhile, the poor pumpkin is looking less and less like a pumpkin. Its skin turns to shades of black, gray and white, with only a few patches of dull orange. Its shape collapses into a heap, then a pile of mush, and then . . . well, no shape at all.

Do you think rot rots? Imagine what your life would be like if things didn't rot. You'd be tripping over all the old pumpkins, not to mention mice, eagles, tomato plants, oak trees and everything else that ever walked, flew, swam or grew upon the earth. Their dead bodies simply wouldn't go away! Worse, their nutrients would be locked forever inside. The energy in the molecules they are made of would be unavailable to any other living things. Rot, properly known as "decomposition," releases all those good vitamins, sugars, proteins, carbohydrates and energy so that they can be used by next year's pumpkin, which will grow from the seeds of last year's pumpkin. Mice and eagles, tomatoes and the trees in a nearby forest can grow and reproduce because nutrients and energy pass through complex food webs from plants to the animals that eat those plants, to other animals that eat those animals.

It's all possible because of rot. So you see, rot doesn't rot. Rot rocks!

Going....

...going...

...gone!

David is the author of > 50 books on math and science, including his newest, rottenest title, Rotten Pumpkin. 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.

MLA 8 Citation
Schwartz, David M. "Rot Rocks!" Nonfiction Minute, iNK Think Tank, 2 Nov. 2017.

2 Comments

What Is a Light Year?

10/3/2022

1 Comment

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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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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Happy Pi Day!

3/14/2022

3 Comments

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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What's the Biggest Number?

Rot Rocks!

What Is a Light Year?

How Old Are You—in Seconds?

Happy Pi Day!

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