What is Infinity?

One of the most used numbers in mathematics (especially hard mathematics!) is:


When most people are asked about infinity, they will probably say something like “It’s the biggest number,” or “It’s totally massively huge.”

Both of these statements, however, are not true!

“What?” you ask incredulously. “Infinity is definitely the biggest number! What number is bigger?”

That is a fair question. Infinity, however, is NOT a number! It’s really a concept.  It means endless. The roots of the word “in-” (not) and “fin” (end) quite literally mean “no end”!

It’s not big. It’s not huge. It’s not totally mega gigantically enormous. It’s endless!

Infinity is a hard concept for the human brain to wrap its mind around. After all, everything we see every day is finite, from the length of our hair to the time in our lunch period to the size of our bed. So when I say something like:

+ 1 = ∞                 or                   + =

You might be like:


But the truth is, it isn’t so complicated. Once you undestand that infinity is not a number, it starts to make sense. Everything plus everything is still going to be everything. Why? Because nothing is LARGER than everything.

If you’re still confused, there are some great resources for explaining infinity. Make sure to check out:

How to explain infinity to a four-year-old

For more fun with math and problem solving, find us at:


Mathnasium is Mathtastic!

Mathnasium student Chili (age 11) wanted to write a blog post for Mathnasium. This is what she wrote:

“Mathnasium can help your kids interact with their future environment!

When you play pool, you have to place the cue at a certain angle to get the ball in the pocket.

In skating, you have to skate at a certain degree when you’re turning or you’ll fall down!

Numbers can help you if you want to become a doctor because you might need to type in the number for the right prescription.

Math is also important to your life because it can help you get good grades on your test.

It can help you balance your checkbook.

Math is for when you don’t get the exact amount of change so you can make sure nobody’s cheating you.

There are variety of numbers (like infinity!) to help you solve math problems.ID-10013484

It can help you get into college.

It can help you turn documents out correctly.

If you are a teacher, math can help you so that you can give the right grades to your students.

It can help you build correct buildings because of correct measurements.

SO JOIN MATHNASIUM NOW!!!!!!!!!!!!!!!!”



Numbers in Nature! – The Golden Ratio

This continuation of our previous article “Numbers in Nature! – The Fibonacci Sequence” will cover another miraculous and seemingly arbitrary pattern that appears everywhere, even in ourselves. We are going to cover the Golden Ratio.

The Golden Ratio = 1 : 1.618

Φ = 1.618034…

Looks complicated, doesn’t it? In fact, the idea is quite simple.

The Golden Ratio was discovered millenia ago in Ancient Greece, and has been found in nature and used in art for centuries since.

The ancient Greeks noticed when they measured a specific length (say, the distance from your shoulder to your elbow) and you multiplied it by approximately 1.618, you got remarkably accurate figure for a related length (say, the length of the entire arm). This may seem like a coincidence, but it kept coming up again and again.

The distance from your foot to your knee multiplied by 1.618? The length of your leg.

Looking at the length of our fingers, each section — from the tip of the base to the wrist — is larger than the preceding one by roughly the Golden Ratio.

Flowers? Golden Ratio.

Pine cones? Golden Ratio.

Fight Patterns? DNA? The human face?



Golden Ratio.


Golden Ratio.

15 Uncanny Examples of the Golden Ratio in Nature


Whether you live in Palo Alto or Redwood City, Menlo Park or Atherton, you can make these observations by yourself! Start with your body and go into your back yard. You’ll be amazed at the patterns you find!

To learn more about math and how it can be used every day, visit us at



Numbers in Nature! – Fibonacci

Numbers and math can often me a source of dread for young students, reminiscent of a stuffy classroom, difficult tests, and lots of homework. However, math is something that transcends school anxiety, and can be found in every corner of our universe. Numbers don’t exist to make school a little harder; they exist to make sense of the world!

Nature often seems to reflect randomness in a world of order. While our cities are ordered in perfect blocks and streets that meet at right angles, nature seems to symbolize disorder; a lack of pattern. How else could you explain the amount of leaves on a tree or the rows on a cob of corn?

However, if we look closer, we find that nothing could be farther from the truth. Nature, just like humans, tend to conform to certain numbers and certain patterns.

Many interesting phenomena can be understood with the help of the Fibonacci Sequence.

Chances are, you’ve heard of the Fibonacci sequence before. After all, it’s pretty straightforward. To get the next number in the sequence, you add the previous number, like so:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89…

The sequence is endless! Although the numbers seem to carry very little meaning, Nature carries these numbers wherever it goes. Let’s look at flowers.


What do lilies and irises have in common? They have three petals. How about buttercups, wild roses, larkspurs, and columbines? Five petals.

Okay, you say, maybe it’s just a coincidence. But look further

8 petals                 delphiniums

13 petals                ragwort, corn marigold, cineraria

21 petals                aster, black-eyed susan, chicory

34 petals                plantain, pytethrum

55, 89 petals          michelmas daisies, the asteraceae family

Do those numbers look familiar?

The Fibonacci Spiral, a famous visualization of the sequence, is often found in shells.


No matter where you look, nature continues to reflect this seemingly arbitrary pattern. Why? How? It’s a mystery both mathematicians and biologists have been trying to solve for centuries. But for now, we can appreciate the mathematical simplicity of the most wild things!

Math Word Problems at Palo Alto’s Happy Donuts!

Happy Donuts on El Camino–Palo Alto’s most beloved donut shop–is famous for their delicious classic glazed pastries. But this tastiness comes with a price: each donut is almost 300 calories, and we all know how hard it is to stop at just one!

Here are some fun donut-themed word problems to try out with your elementary or middle schooler during your next trip to Happy Donuts:

Happy Donuts Word Problems

happy donuts palo alto math word problems mathnasium


  • You eat two extra-glazed donuts at 400 calories each. Your friend Sharon eats three powdered donuts, which are 300 calories each. Who has eaten the most calories?
  • You get a box of a dozen donuts  from Happy Donuts. 6 are glazed, 3 are chocolate, 2 are jelly-filled, and 1 has chocolate sprinkles on top. If you choose one from the box at random, what is the probability you will get a jelly-filled donut? You eat this donut, and reach into the box again. What is the probability you will get the second jelly-filled?
  • If you’re supposed to eat 2,000 calories per day, and you eat 500 calories worth of donut holes, how many calories do you have left? What fraction of your daily caloric intake have you already eaten? Can you convert this to a percentage?
  • You bring two dozen donuts to class, and your classmate Jackie eats 1/4 of the donuts! How many did your friend eat? How many are left for the class?
  • You just ate 4 mini donut holes at 75 calories each. If running burns about 150 calories per hour, how many hours will you have to run to burn off those delicious donut holes?
  • If each donut is exactly 300 calories, how many calories are in a box of one dozen donuts?

You get the idea! Try making up your own donut-themed math problems on the spot and quizzing your kid during your next trip to Happy Donuts! These problems are fun to solve and help strengthen your child’s understanding of word problems, which many children struggle with. Post your own creative math problems below!

> Learn more about Math Tutoring in Palo Alto / Menlo Park

~ Mathin’ Catherine 6/2013

Palo Alto Impressionist Kids: How to Make a van Gogh Perspective Drawing!

Vincent van Gogh is famous for his impressionist paintings such as “Starry Night” or “Cafe Terrace at Night,” but did you know that all of his painting use math in one way or another? A common instance of math in his paintings is the use of perspective, or use of a “vanishing point.” Making your very own perspective drawing with a vanishing point is a fun and easy way to mix math and art together, and get your child interested in the many different applications of math. Here are some tips on how to help your child make his or her very own perspective drawing; all you need is a ruler, paper, pen, and some imagination! Kids all over Palo Alto love this project; it’s easy and a creative way to engage your child in math. Without further ado, 5 steps to making your very own van Gogh-inspired perspective drawing:

How to Make a Van Gogh-Inspired Perspective Drawing

perspective math van gogh kids art project

  1. On your sheet of paper, use a ruler to draw a line straight across the center of the paper, like the one to the right.
  2. Somewhere on the line near the middle, make a small dot. This is your “vanishing point.”
  3. Make two lines crossing through the dot to make an “X” shape.
  4. Use these lines as guidelines to make buildings, trees, or–well–anything you want! Here is an example to the right you could try!
  5. Color your masterpiece and add details!

Congratulations, you’re done! Hang or frame your beautiful van Gogh masterpiece on your kitchen fridge or bedroom wall! Have fun with this cool perspective project and happy “mathing!”

~ Mathin’ Catherine, 6/2013

> Learn more about Math Tutoring at Mathnasium of Palo Alto – Menlo Park


Hey Palo Alto Parents! Here’s a Fun M.C. Escher-Ispired Art Project for Kids!

M.C. Escher is world-famous for his beautiful tessellations, so here at Mathnasium of Palo Alto-Menlo Park we’ve created some easy instructions for how to make your very own tessellation in this great math-related art project! For parents that can’t exactly recall freshman year geometry as if it were yesterday, a tessellation is a a pattern using a single shape, without gaps or overlapping. Tessellations are a fun and creative way to make math interesting outside the classroom!

Math-related art projects are a cool way for kids to get interested in math and art, and help them understand the connection between math learned in the classroom and math used in real life. Below are the instructions, and be sure to check out our previous post for more math-centric art projects for elementary and middle schoolers!

How to Make an M.C. Escher Tessellation

tessellation math math-related art project mathnasium

Tessellation instructions

  1. Start out with a drawing a square or rectangle, like the one shown below. Use a ruler to make sure all sides are even.
  2. Add shapes coming off of or going into your shape. Whichever shapes you choose to add to/cut out of the rectangle, do the opposite to the other side, as shown.
  3. Cut your new shape out, and use it to trace again and again on another sheet of paper, to make a tessellation!
  4. Color, and you’re finished! Congratulations, you just made a tessellation!

Tessellations are a great math-related art project because you can decide how simple, or how intricate, you want your design to be! Have fun with this great and easy art project with your kids!

~ Mathin’ Catherine, 6/2013

> Learn more about Math Tutoring at Mathnasium of Palo Alto – Menlo Park

5 Fun Math-Related Art Projects for San Carlos Elementary & Middle School Kids!

Math and art have always been linked closely, so why not try exploring this link in a fun way with your San Carlos kids? Math in art is everywhere–just look at M.C. Escher’s cool geometric tessellations, or the use of proportions in Leonardo Da Vinci’s “Virtruvian Man.” By incorporating math into fun art projects, you can increase your child’s love of learning, and their creativity when exploring math! Making math fun is an important key to your child’s success in the subject, so why not up the fun quotient with some new math-related arts and crafts? Below are five tips to make this summer an art and math filled experience:

tessellation math math-related art mathnasium

Tiled Hexagon Tessellation by Urban Hafner via Flickr

5 Fun Math-Related Art Project Ideas for Kids

  • Make a tessellation just like M.C. Escher or the one above! Here’s a link explaining how to easily make an impressive tessellation; all it requires is a sheet of paper, some scissors, and some markers or colored pencils.
  • Create a 3D sculpture of one of the five platonic solids! They’re a blast to create and make great decorations for any room. Directions can be found here.
  • Create a compass mandala! These are fun because they can be as complicated or simple as you choose to make it, and all you need is a compass, pencil, and some coloring materials! Click here for the simple directions.
  • Here’s an edible math treat! Use toothpicks and marshmallows/gumdrops to create cool 3D shapes, like cubes, pyramids, and cones, then branch out to see other shapes you can make! See who can get the biggest/most complex sculpture without collapsing, then enjoy eating the losing sculptures.
  • Make a number pattern graph like the one found here! Test out different graphs to find the different exponential curves you can make.

These art projects are fun and help strengthen the connection between math and the real world. Try taking your kids to an art museum afterwards, and see if they can point out any math they can see in the sculptures, paintings, and photographs! Comment to let us know which of these math-related art projects worked for you.

~ Mathin’ Catherine, 6/2013

> Learn more about Math Tutoring at Mathnasium of Palo Alto – Menlo Park