Here’s an example: Let’s say you need to build a fence around your tomato plants. If you know that the bed is 4 feet by 2 feet, how much fencing do you need? (Yes, I’m ready for spring and summer and fresh veggies. Will this cold weather ever end??)

This is a perimeter problem. Some of you might write down the formula for perimeter of a rectangle: P = 2l + 2w. But I’d be willing to bet that most of us simply add: 4 + 2 + 4 + 2 = 12 feet. No formula needed, right?

But what if we turn the problem on its head? Let say you have 12 feet of fencing, and you’re building a tomato plant bed that must be no longer than 4 feet. How wide can the bed be?

Again, there are tons and tons of ways to approach this problem. One is with literal equations. What do you know about the information you have? The perimeter and the length. What are you solving for? The width.

P = 2l + 2w

The object of the game is to solve the formula for w, in terms of P and l. (Stay with me here. I promise this is easier than that previous sentence made it sound.) To do that, you need to get w by itself on one side of the equation. This is where the algebra comes in.

The most important rule about solving algebraic equations is this: Whatever you do to one side of the equation, you must do to the other. Period. End of Sentence. Amen. Shalom. To do that, you need to undo the operations. It’s like taking something apart. Here’s how it works:

Don’t panic! This is not as messy as it looks. All you need to do now is substitute what you already know, use the order of operations to simplify, and you’ll have w.

So the width of the tomato bed must be 2 feet. My point is not that you must always solve a problem like this one in this way. Nuh-uh. My point is that there’s algebra behind this problem – no matter how you solve it. And whether you like it or not.

How would you have solved this perimeter problem? See if you can spot the algebra in your approach. And share in the comments section.

I am so pleased to be Meagan Francis‘s guest this month on The Kitchen Hour, her 45-minute podcast for parents on the go. We talk about math anxiety, math education and how to encourage our kids to embrace math — while overcoming our own fears. Listen and/or download the podcast at The Kitchen Hour.

The post It’s Not Tomato Season Yet, But You Still Need Algebra appeared first on Math for Grownups.

Ah, the cookie exchange!  What better way to multiply the variety of your holiday goodies.  (You can always give the date bars to your great aunt Marge.)

The problem with this annual event is the math required to make five or six dozen cookies from a recipe that yields three dozen.  That’s what I call “cookie exchange math.”

Never fear! You can handle this task without tossing your rolling pin through the kitchen window. Take a few deep breaths and think things through.

To double or triple a recipe is pretty simple — just multiply each ingredient measurement by the amount you want to increase the recipe by.  But it’s also pretty darned easy to get confused, especially if there are fractions involved.  (And there are always fractions involved.)

The trick is to look at each ingredient one at a time.  Don’t be a hero!  Use a pencil and paper if you need to.  (Better yet, if you alter a recipe often enough, jot down the changes in the margin of your cookbook.)  It’s also a good idea to collect all of your ingredients before you get started.  That’ll save you from having to borrow an egg from your neighbor after your oven is preheated.

Read the rest here — and you’ll avoid fractions-related, messy kitchen mistakes.

While you’re at it, check out this interview I did with fantastic candy-maker, Nicole Varrenti, owner of Nicole’s Treats. (I love her chocolate mustaches, personally.) It shouldn’t be any surprise that she uses math daily.

Finally, if you have some holiday-related math questions, would you mind sharing them with me? What trips you up — mathematically — at this time of year? Comment below!

The post Time for Holiday Cookies — and Fractions appeared first on Math for Grownups.

Let’s start by with the bees. In research for a magazine assignment, I’ve done some reading about bees lately, and once again, I’m in absolute awe. These little guys are the linchpins of our ecosystem in a lot of ways. Not only does their pollen-collecting insure the reproduction of a variety of plant species (and therefore the survival of critters that depend on these plants), but their colonies are efficient little factories that seem to mirror human manufacturing — from the dance the workers do to relay directions to the best pollen to the efficiency of their job descriptions.

And then there are the hives. If you think of the bees as efficient — and they are — you can deign why the hive is made up of tiny hexagons. (Remember, a hexagon is a six-sided figure.) Not wanting to waste any space whatsoever, the bees figured it out: instead of making circular cells, which leave gaps around the sides, they create a tessellation of hexagons, which leave no empty space at all.

(A tessellation is the repetition of a geometric shape with no space between the figures. Think M.C. Escher or a tile floor.)

The same concept applies to gardening. Why waste space? As Cristina pointed out, choosing a hexagon-shaped planting scheme, you’ll get more plants in your beds.  And if you’ve got an outlaw garden, like Cristina, it’s best to make the most of your space! Here’s how:

In regular rows, you plant 6″ apart in only two directions, getting nice, even rows. But if you consider six directions, you’re replicating the hexagon, instead of a square — and as a result maximizing your space (just like the honey bees). Cristina describes it as planting on the diagonal. Or you can think of each plant at the center of the hexagon.  Then you can plant the others 6″ from the center in six directions — creating the vertices of the hexagon. (If you’ve ever looked carefully at a Grandmother’s Flower Garden quilt pattern, this idea might jump out at you. Not only is each plant the center of a hexagon, but it’s also the vertex of another hexagon.)

Did you see what I did there? Math can be described in a variety of ways! Look at the second diagram carefully, and see what jumps out at you — the hexagons or the diagonal rows?

So there you have it. We can learn a lot from a bee. And I can already think of times when this can be useful in other areas. How many more cookies can you fit on a cookie sheet, if you arrange them diagonally (or in a hexagon shape) rather than horizontal rows? What about kids desks in a classroom?

Where can you apply the hexagon to make your space more efficient? Share your ideas in the comments section!

The post The Mighty Hexagon: Let bees help you garden appeared first on Math for Grownups.

In the garden, math is everywhere. There’s arithmetic and subtraction, which gardeners use to estimate how long it will take for a tomato to ripen or a seed to sprout. There’s multiplication, which helps gardeners calculate expected yields. And, there’s higher math too. Lots and lots of higher math.

Yesterday, for example, I used a measuring tape and a bit of high school geometry to confirm that my tomato trellis would be a nice (right-angled) rectangle, rather than a slightly askew parallelogram. I also used an online calculator, because figuring out the square root of 10,116 isn’t especially easy to do by hand. I knew I’d get a number close to 100, but I wanted to be sure.

Turns out that the square root of 10,116 is 100.57832768544127. I rounded to 100.5, because my measuring tape isn’t quite that fine-tuned.

If you haven’t guessed yet, I was using the Pythagorean Theorem: a² + b² = c². As an avid DIYer, I use this formula a lot. It’s a great way to be sure that your project will be square, with four right angles. That’s essential if you’re building any sort of box, especially if you’ll be adding a door later. A slight skew away from 90° can create all sorts of trouble.

In this case, the motivation is all aesthetics. This trellis could work fine as a parallelogram. The tomatoes wouldn’t even notice. But, I would.

So, here’s how I did it. The trellis is 96 inches tall and 30 inches wide. Those are our a and b sides. Putting them into the equation, we get 96² + 30² = c². That works out to

9216 + 900 = c²

10,116 = c²

This is when I googled “square root,” in hopes of finding an online square root calculator. I knew it would come in close to 100, because 100 • 100 = 10,000. But, I wanted to be as exact as possible. That’s where the online calculator came in handy. The answer — 100.57832768544127 — was more precise than I really needed. 100.5 inches is plenty good enough when building trellises in the garden.

With that number in mind, I measured the diagonal from top to bottom on both sides of the trellis. One side measured about 100.25 inches and the other measured about 100.75 inches. A slight adjustment, and both sides measured 100.5 inches. The trellis was square. Success!

Here’s the plan for the trellis. You can see where the right triangle would go:

(Cristina has a great post detailing the step-by-step process for building her trellis, including a downloadable pdf of her plans. Check it out here.)

Trellises aren’t the only place we use and see geometry in the garden. The Pythagorean Theorem is a great help to gardeners who want to ensure their garden beds and paths are perfect squares or rectangles, for example. And, equilateral triangles — three equal sides — provide guidance when planting the garden. While most books tell us to plant our vegetables in rows that are square to each other, that’s not the best way to maximize our garden space. No. Instead, plant your rows on a diagonal, using an equilateral triangle as your guide, and you will be able to fit more plants into the same amount of space. Like this:

See how a series of six triangles creates a hexagon in the diagonal planting pattern? That’s where the extra space efficiency comes in; you’re basically planting on a hexagonal pattern. And, as bees already know, the hexagon is the most efficient shape.

Even plants have geometry. All members of the mint family have perfectly square stems, like this bee balm:

Sedges — a grass-like bog plant — have triangular stems. Some plants, like dogwood and maple trees, follow a perfect symmetry with their leaves. These are known as opposite plants, because their leaves form opposite one another on their branches. Alternate plants, on the other hand, form their leaves singularly or in groups, on alternate sides of the branch. Other plants grow their leaves and flowers in whorls or rosettes:

The dogwood has opposite leaves.

Virginia Sweetspire has alternate leaves.

The leaves of the culversroot are in a rosette pattern.

And, the Fibonacci Sequence is everywhere:

The pattern of the yellow spirals in this chamomile are based on the Fibonacci sequence

Thank you, Cristina! My advice to you, dear reader: do not miss her blog, Outlaw Garden; it’s funny, informative and really, really clever. Do you spend time in the garden? What kind of math do you use and see while tending your plants? If you have questions, don’t hesitate to ask in the comments section. Don’t worry, I’ll ask Cristina to come by to respond. (It’ll be better that way.)

The post Garden Geometry: A guest post from the Outlaw Garden appeared first on Math for Grownups.

That was the last time we ever had a garden, but it certainly wasn’t the last time my mother canned. As a little girl, I never had store-bought green beans, canned tomatoes or pickles. These were all preserved in Ball jars and stored in the basement for year-round eating. And while I’ve never canned myself, I am interested in at least pickling a few cukes this summer.

So where’s the math? Well, it’s everywhere in canning. Just like with cooking, preserving foods requires recipes — and then there’s the part about taking a huge pile of fruits or veggies and divvying them up into a series of jars. Yep, math.

See, canning is hot, hard work. In the middle of summer, you need to boil large pots of water, keep the jars warm in a hot dishwasher, the oven or a water bath. The last thing you want to do is run out of jars or lids in the middle of this entire ordeal. Doing the math upfront means you can get in and out of the kitchen without an added trip to the store (or your next door neighbor’s).

Turns out there are easy-to-follow charts and tables for dealing with yield. But if your garden — or trip to the farmer’s market or pick-your-own farm — doesn’t yield the exact amount on the chart, you’ll need to do a little math.

Drew’s humble green-bean patch is overflowing. After convincing the kid down the street to pick all of them (for a small fee, of course), he sits down in front of the television to snap them. (The Olympics and snapping green beans are a perfect combo.) At the end of a few hours, he estimates that he has about 16 pounds of green beans. Whoa.

If he cans all of these beans, how many quart jars will he need? Turning to a trusted web source, he learns that a quart jar will hold about 2 pounds of green beans. Easy math: 16 ÷ 2 = 8. So he’ll need 8 quart jars.

He’s got 15 quart jars in the basement, so the green beans are covered. But he also needs to put away his tomatoes. Will he need to buy more jars?

After canning the green beans (and not using the f-word even one time — such restraint!), he considers those ruby red fruits. This time, he picks them himself, ending up with about 15 pounds. Consulting his yield chart again, he is faced with another decision: crushed or halved/whole? Canning tomatoes is a little more work, since he’ll need to skin them first. He decides to look at the yield for each option before making up a plan.

Crushed tomatoes yield 2.75 pounds per quart, while halving them or leaving them whole yields 3 pounds per quart.

Crushed: 15 pounds ÷ 2.75 pounds= 5.5 quarts (about)

Halved/whole: 15 pounds ÷ 3 quarts = 5 quarts

He’s already used 8 of his 15 quart jars, leaving him with 7. So he’ll have plenty of jars either way. If he crushes the tomatoes, he’ll need a couple of pint jars (because there are 2 pints in a quart). So, he decides to leave the tomatoes whole (or cut them in half, if necessary).

And with two quart jars left over, he decides it’s time for pickles!

Do you have plans to can anything this summer? Share your resources, tips, recipes and more in the comments section. I need inspiration!

A programming note: I am changing my posting schedule a little — at least for the summer. Math at Work Monday interviews will now appear twice a month, rather than every Monday. If you have suggestions of folks I should interview, let me know!

The post Preserving the Harvest: Canning with Math appeared first on Math for Grownups.

From my days as my high school yearbook editor, I know that there’s a little formula used to find the number of pages that a book can have. If you need to have a certain number of pages (at least), you’ll need to employ that tidbit of information. But first you must know how many pages you’d like to have in your book.

Your teenager is headed off for a two-week long camp in the woods. She loves to write in a journal, and you’d like to make her a special book to take with her. If she uses three pages per entry, how many pages does her journal need to have?

Let’s assume she’ll be journaling every day of her two-week stay. And let’s assume that she’s leaving on the last day. So that means she’ll journal for a total of 13 days (that’s two weeks, minus one day), and she’ll need a total of 3 • 13 or 39 pages.

But here’s where you’ll need a little book-making insider information. Books are actually made up of signatures, which are sets of folded paper. You can put as many pieces of paper you want in a signature, and you can put as many signatures you want in a book — but the resulting page count will always be a multiple of 4.

(Don’t panic if you don’t remember what a multiple is. Look carefully at the word. You’ll probably notice that multiply is a root, which may cause you to think of multiplication. You’re on the right track. A multiple is a product of two numbers. So the multiples of 4 are: 4, 8, 12, 16, 20, etc. That’s because 4 • 1 = 4, 4 • 2 = 8, 4 • 3 = 12… well, you get the picture.)

In your book, the number of pages must be a multiple of 4, and you need at least 39 pages. Your first question: Can my book have exactly 39 pages? Nope. That’s because 39 is not a multiple of 4.

You need to find a number close to 39 that is a multiple of 4, and you have two obvious choices: 36 (4 • 9) and 40 (4 • 10). Of course, you’re going to chose 40; otherwise, your daughter won’t have enough pages in her book. (Better to have too many than not enough.)

Now you can decide how to create your signatures. I leave those details to the experts. Besides, you need to choose a book style first. Take a look at these great resources I found on Pinterest. Pick one, and have fun!

The Pioneer Woman Makes a Book (from a granola bar box)

Mini Jotter How-To from The Guilded Bee (by way of oh hello friend)

Flower Pressing Book from Family Fun

Teeny-Tiny Leather Spell Book from Ruby Murray

Rainbow Art Book

Have any tips for making memory books? Share them in the comments section!

The post Counting Pages: Make a memory book appeared first on Math for Grownups.

Hanging pictures can be a tricky business. If you’re not careful, your foyer can look like a hall of mirrors—with crooked photos of your wedding party alongside drawings that your kid made in kindergarten. Not to mention the holes in the drywall from when you realized that you hung your college diploma so high up the wall that only a giant could read it.

Not exactly the look you were going for?

You may not want to face it, but a tape measure, pencil, and yes, even a level, are your best buddies in home decorating. And hanging anything on your walls is no exception. Let’s look at this in a bit more detail.

Mimsy Mimsiton is thrilled to have finally received the oil portrait of her dear Mr. Cuddles, a teacup poodle who is set to inherit her large fortune. The painting will look fabulous above the marble fireplace in the west-wing lounge of her mansion.

But drat! The museum curator Mimsy has on retainer is in Paris, looking for additions to Mimsy’s collection of French landscapes. (She’s redoing the upstairs powder room and wants just the right Monet to round out the décor.)

But the painting must be hung before Mr. Cuddles’s birthday party. His little poodle friends would be so disappointed not to see it! There’s no way around it; Mimsy’s poor, overworked House Manager must hang the painting herself.

Luckily, House Manager is no stranger to the DIY trend, and Butler will be there to help. The two meet in the lounge, where the painting has already been delivered—along with a stepladder, a tape measure, and a pencil. Once House Manager marks the spot, Handy Man will come along to safely secure the painting to the wall.

House Manager and Butler get to work. First they measure the painting: With the gilded frame, it’s 54″ tall and 60″ wide.

Next, they turn their attention to the space above the mantle. House Manager climbs atop the ladder, while Butler holds it steady. From the ceiling to the top of the mantle is 84″.  The width of the mantle is 75″.

Climbing down from the ladder, House Manager notes that the painting will certainly fit in the space allotted. She knows from experience that it is to be centered over the mantle. However, Mimsy will have a fit if the painting is centered vertically—between the ceiling and the mantle. No, the bottom of the painting must be exactly 12″ above the mantle.

So how high should Handy Man install the picture hanger?

To find out, House Manager must add 12″ to 54″ (the height of the painting). The top of the painting should be 66″ above the mantle.

House Manager grabs her tape measure again and removes the freshly sharpened pencil from behind her ear. Then she climbs the ladder. Starting at one end of the mantle, she measures 37½”—which is half the width of the mantle. She makes a barely visible pencil mark at that point.

Then from there, she measures up the wall to 64″. Again, she carefully makes a faint pencil mark.

If House Manager stopped here—leaving that small mark for Handy Man to hang the portrait—she’d probably be out of a job. That’s because she’s merely marked the top of the frame, not where the hanger should be secured.

She descends the ladder and goes back to the portrait. Turning it around, she notices the picture wire that has been stretched from one side to the other. She hooks her finger under the center of the wire and pulls up gently—creating an angle, as if the picture wire were hanging on a nail. Now an angle is a two-dimensional figure formed by two lines (called rays) that share a common point. Hereʼs an easier way to remember this: An angle looks like a V.

If she can measure the distance from the top of the frame to the vertex—the point where two sides of an angle meet—she’ll be in business.

There’s just one more thing to consider: Is the vertex of the angle too far to the left or too far to the right?  For the painting to hang straight and be centered on the mantle, the vertex must be located at exactly half the width of the portrait.

House Manager uses her tape measure to find the length of each leg of the angle. In other words, she measures the distance from one end of the picture wire to the vertex of the angle and then the distance from the vertex of the angle to the other end of the wire. If the vertex is centered properly, the legs of the angle will have the same length.

Moving her finger ever so slightly, House Manager centers the vertex of the wire angle—and measures from that point to the top of the picture frame: 9″.

She now can make the final mark for Handy Man. She climbs the ladder for the third time and measures 9″ from the mark she made earlier. Again, being very careful, she makes a tiny mark on the wall.

House Manager’s work is done. If anything goes wrong now, it’s Handy Man’s fault.

She folds up the ladder and gathers her supplies. Then she’s off to order beef cupcakes for Mr. Cuddles’s party.

Any questions?  Ask them in the comments section.

The post Pretty as a Picture: Using math to hang your art appeared first on Math for Grownups.

When I decided to organize my junk drawer two weeks ago, I did what most folks do — I purchased a drawer divider set with a variety of different sizes.  The idea is to group like things together.  The pencils go in one section, pens in another.  Littler compartments hold paper clips and Box Tops.  And the biggest container is for my precious scissors, which seem to go missing at least once every other day.

In fact, this is the No. 1 tennet of organization: A place for everything and everything in its place.  If I have a designated spot for my daughter’s erasers, they won’t be strewn around my kitchen counters or tossed into the silverware drawer.  (And she won’t be screaming in a fit of last-minute homework, “I can’t find an eraser!)

At least that’s the idea.

And that idea is as old as dirt.  In fact, it has its roots in mathematics, specifically set theory, which wasn’t formalized until Georg Cantor, a German mathematician, published an article on the subject in 1874.  This blew the socks off of the mathematics community — mainly because he proposed that there are two kinds of infinities.

But I digress.

Kindergarteners learn about set theory, when they circle like things on a worksheet.  And many parents probably wonder why this is such a big deal.

In short, set theory is the basis of our numerical systems — among many other things.  Mathematics craves order.  Knowing why things are alike or different can help us solve problems quickly and effortlessly.  Just like knowing where my scissors go (and putting them there) makes it easier for me to find them later on.

As an example, let’s look at the set of whole numbers.

{0, 1, 2, 3, 4, 5, 6, 7, … }

(Okay, just so no fancy-schmancy mathematician jumps down my throat, I have to note here that there is some disagreement about whether 0 belongs in this set.  But for most of the rest of the world, that’s a point not worth arguing about.)

When you know the set of whole numbers, you can determine whether or not a number is in that set.  For example:

0.25 is not a whole number

60% is not a whole number

π is not a whole number

-17 is not a whole number

But: 6,792,937 is a whole number

But why do you care? Honestly, I think the biggest reason is so that you can talk about math.  In this case, set theory tells us the difference between whole numbers, integers, decimals, rational numbers, etc. — even if you don’t remember what all of these are.

(And those of us who know a little bit about math also know that whole numbers are in the set of integers, which are in the set of rational numbers, which are in the set of decimals.)

So this is how math is like organizing.  Both depend on set theory.

I’m not saying that you have to be organized to do math.  Lord knows I’m not.  But the underlying organization of math points to big clues about how it’s done.  Even more basic sets, like geometric shapes can apply in our everyday lives.

The bottom line is this: If  you think  you can get your house or office or car organized (and I believe you can!), you can certainly organize all of what you know about math and put it to good use.  That way, you’ll always know where your area of a triangle is.

How do you think about the structure of numbers or shapes or arithmetic operations?  This points to your intuitive understanding of set theory.  Share your thoughts in the comments section!

The post Ready, Set, Organize! appeared first on Math for Grownups.

How many times have you uttered these words or heard someone else say them?  You and they are not alone.  Getting organized is one of the most common New Year’s resolutions.  But like losing weight, it’s easier said than done.

But how do you manage this daunting task? If you’re inclined to take a week off of work, with high hopes of a sparkling, organized home after five long days, you may want to reconsider.  If you’re not already organized, why would you want to spend so much time cleaning out your linen closet and kitchen cabinets?

On this point, the experts agree: a little goes a long way.  So most suggest that devoting only 15 minutes a day to organization can yield big benefits.  Let’s take a look at the numbers.

If you devote five days, for (let’s be generous) 10 hours a day, you’ll end up working 50 hours total, right?  (That’s 5 days x 10 hours or 50 hours.)  And you’d probably also have a sore back and a week’s worth of vacation lost to your label maker and plastic bins and lids.

But what if you committed to 15 minutes a day, 5 days a week?  How much time will you have spent?

15 minutes x 5 days = 75 minutes

75 minutes ÷ 60 minutes = 1.25 hours (or 1 hour and 15 minutes)

Gosh, I spend more time in a week figuring out what’s for dinner.

So what if you started on January 1 and stuck with it throughout the month?

There are 22 weekdays in January

15 minutes x 22 days = 330 minutes

330 minutes ÷ 60 minutes = 5.5 hours

That’s less than the time it would take for you to watch the first two films in the Lord of the Ringstrilogy!

So let’s take this a bit farther.  If you managed to keep this resolution for an entire year, how much time will you have spent organizing?  Let’s assume there are 250 workdays in the year.  (You’re not going to organize on a holiday are you?)

15 minutes x 250 days = 3,750 minutes

3,750 minutes ÷ 60 minutes = 62.5 hours

So by devoting a mere 15 minutes a day to organizing, you can end up spending more time over the year than if you took a week off and worked on the task for 10 hours a day.  Plus, I guarantee you’ll be much more relaxed.

But what can you accomplish in 15 minutes?  Here’s a short list:

• Cleaning out your junk drawer
• Going through seasonal clothes and deciding what to give away, toss or keep.
• Alphabetizing your spice rack.
• Culling through your kids’ artwork and filing or scanning special pieces.
• Scanning your bookshelves for titles you’re ready to part with.
• Setting up a spot for your mail, keys, purse and jacket.

By the end of one week, you could have a tidy junk drawer, trimmed summer wardrobe, room on your bookshelves and a regular spot for your keys.  By the end of the year?  Who knows what you could accomplish!

Have any organizing tips to share?  Post your ideas in the comments section.  I’ll bet I (or someone else) can find the math in that technique!

The post Getting organized bit by bit appeared first on Math for Grownups.

But I still have this stack of gifts to wrap.

I figure there are two kinds of people in the world: those who painstakingly dress each gift with crisp paper and color-coordinated bows; and those who haphazardly slap on some paper and call it a day.  I’m not so precise about most things, but you can put me in the first camp as far as gift wrapping goes.

Still, I’m mighty lazy.  I don’t measure out paper or use double-sided tape.  Instead I use a little bit of geometry to get my gifts just right.  It’s not hard at all.

The trick to a perfectly wrapped gift is to have just enough — not too much and not too little — paper to cover the package.  And to do that, use a box, if the item is oddly shaped.

Now consider the width of the box.  Line the box up on one end of the paper, like this:

And then turn the box up on the left edge, over onto the other large side and up again on the last edge, like this:

You want to have some left over paper on the left.  This will overlap so that there’s no gap in the seam.

Now you can look at the length of the package.  This is where things get a little tricky.  You need a little more than half the height of the package.  (I just eyeball it, but you can be more precise, if you want.)  You’re ready to cut.

So your paper is cut.  (Did you notice that throughout that easy process, you thought about the width, length and height of the box?  That’s the geometry at work here, folks.)  It’s time to start wrapping.  Turn the box upside down onto the paper.  This way, the seam will be on the bottom of the box.

Wrap one of the long sides of the paper over the box and secure with tape.

Do the same with the other side, making sure that the paper is tightly wrapped around the box.

Now it’s time to address the sides of the gift.  Fold down the top paper, so that it’s flush against the box.  If you’ve eyeballed your measurement correctly, the paper won’t be too long or two short.  Then fold in each side of the paper, making little angles.  Crease each one with your fingernail.  Then fold the last flap up, so that it looks like an envelope.  Use tape to secure that flap.

The other side is much easier, because now you can put the box up on the side you just wrapped.

Once everything is folded and taped up, use your fingernail to make sharp creases along each of the edges of the box.  Add a bow — I like using wired bows made of fabric, because they’re easy to manage, and I can reuse them again next year.  Ta-da!  The perfect gift!

Do you have a gift-wrapping technique to share?  If so, tell us in the comments section.

The post Using Math to Wrap Gifts appeared first on Math for Grownups.