Category: Mathematics

How Old Are You—in Seconds?

4/8/2022

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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Happy Pi Day!

3/14/2022

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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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Amazing Grace

3/1/2022

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Jan Adkins
The Explainer General

She was 15 pounds below minimum weight for the Navy when she joined, but she had a mighty mind. Admiral Grace Hopper changed the Navy. And your world.

She graduated from Vassar College in math and physics then took a doctorate from Yale in math. She joined the Navy in World War II because it needed mathematicians to build the massive machines that computed tables of distance, gun elevation, projectile weight, windage and other factors for precise naval gunnery. Almost immediately she saw something other mathematicians didn’t see: computers could talk.

They weren’t just number crunchers to Grace. They could do much, much more if they were given a simple language that would bring the advantages of gigantic computing power and enormous data storage to common uses.

While working on the early computers she developed a “compiler,” a kind of translating machine that turned plain-language needs into a set of mathematical commands that retrieved number data from storage banks, performed thousands or millions of math operations, and provided real-world answers.

     In 1959 she was crucial in devising the first broad-based computer language, COBOL (COmmon Business Oriented Language). It is the root of the many computer operating systems we use today.

Then-Captain Grace worked with the National Bureau of Standards to develop self-testing capabilities so a computer could “de-bug” itself. She coined this word when she extracted a fried moth disrupting one of her computers.

   She led the Navy away from a few giant computers to interconnected, smaller, scattered computers, opening the door to the internet. You are reading plain language words from my small computer on your web-connected small computer. Thank you, Grace.

In 1985, at 79, she was promoted to rear admiral of the United States Navy Reserve. She said, “The most important thing I've accomplished, other than building the compiler, is training young people. They come to me, you know, and say, 'Do you think we can do this?' I say, ‘Try it.’ And I back 'em up. They need that. I keep track of them as they get older and I stir 'em up at intervals so they don't forget to take chances.” She died in 1992 at 85.

     Admiral Grace Hopper received many awards and decorations but the Navy’s most sincere tribute came in 1996 when it named the guided missile cruiser DDG-70, USS Hopper. Naturally, its sailors call their ship “Amazing Grace.”

Commodore Grace M. Hopper, January 1984. By James S. Davis via Wikimedia Commons

Secretary of the Navy, John Lehman, right, promotes Capt. Grace Hopper to the rank of commodore in a 1983 ceremony at the White House. President Ronald Reagan is at the left. US Department of Defense

Grace Murray Hopper at the UNIVAC keyboard, c. 1960. She was a pioneer in developing computer technology, helping to devise UNIVAC I. the first commercial electronic computer, and naval applications for COBOL (common-business-oriented language). Smithsonian Institution

While she was working on a Mark II Computer at a US Navy research lab in Dahlgren, Virginia in 1947, Hopper's associates discovered a moth stuck in a relay and thereby impeding operation, whereupon she remarked that they were "debugging" the system. Here is the famous bug -- if you want a closer look at this famous bug, its remains can be found in the group's log book at the Smithsonian Institution's National Museum of American History in Washington, D.C.

Jan Adkins successfully tackles the art and science of 10,000 years of bridge building and imparts a lot of historical drama along the way. The process is given fascinating life in this accessible study, wonderfully illustrated by Jan Adkins himself. Ranging from ancient Rome to the present day, from simple log bridges to marvels of industrial technology, and from well-known landmarks to little-known feats of engineering and art, this book gives readers a new appreciation for that most familiar of structures, the bridge.

Jan Adkins 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
Adkins, Jan. "Amazing Grace." Nonfiction Minute, iNK Think Tank, 25 Jan. 2018,
www.nonfictionminute.org/the-nonfiction-minute/amazing-grace.

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If the Earth Were a Button

1/27/2022

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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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How Old Are You—in Seconds?

Isaac Newton's Wonder Years

Happy Pi Day!

Amazing Grace

If the Earth Were a Button

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