But My Kids Hate Math

Well, maybe your kids don’t hate math, but parents struggle with getting their kids excited and confident about learning math. Remind your kids that math isn’t only about formulas and numbers, but it’s also about fun real-life examples.

You can do this by bringing math home from the classroom and into their daily lives. Kids will get excited when they can see the numbers and formulas applied in everyday examples.  Need ideas? Check out our blog to help your kids discover mathematical concepts through hands-on exploration and play!

Lemon Zest and the Surface Area of a Sphere

Lemon Zest and the Surface Area of a Sphere

I was recently asked to bring a cake to a reception on very short notice. Luckily, I found this recipe for Olive Oil Cake  by Marcella Hazan, for which I had all the ingredients. I had two small lemons left in the fridge, and I conveniently assumed that the zest of both of them will be equivalent to the “zest of one lemon” required by the recipe. Was I right?  Just out of curiosity, I asked myself: What would be the size of the hypothetical one lemon which would yield the same amount of zest as my two small lemons? Would this be a gargantuan lemon of mythical size, or just a regular looking fruit? This was easy enough to determine, since my two small lemons were nearly spherical, with diameter of about 2 inches: The lemon zest layer is so thin, that its amount can be measured by the surface area of the lemon times its thickness. Using the formula for the surface area of a sphere of radius r, Surface Area =4πr², and the fact that our lemons have a radius of about an inch, we have that the surface area of each lemon is about 4π square inches. So the surface area of the two small lemons is 8π square inches. How large a single lemon would have to be in order to have surface area of 8π square inches? Its radius, R, is given by this equation: 8π = 4πR² So R=√2≈1.4 inches. That’s not that big! At just 2.8 inches diameter, this hypothetical lemon would be well inside the range of lemons supplied by Sunkist growers. So it was a good call to replace... read more
In the footsteps of Archimedes: celebrating Pi day

In the footsteps of Archimedes: celebrating Pi day

Nowadays, thanks to modern day computers, we have instant access to the approximation of π (the ratio of a circle’s circumference to its diameter) to any degree of accuracy. But back in antiquity, getting a good approximation of π was elusive and difficult. Over 2000 ago, the Greek mathematician and scientist Archimedes derived an accurate approximation of π using polygons to approximate a circle. Let’s follow in his footsteps with Geometiles as our tool. We’ll start by approximating the circle with a square, then a regular hexagon, and finally a  regular dodecagon (that’s a 12-sided polygon; dodeca means 12 in Greek). You can see that the more sides our regular polygon has, the rounder it is. In fact, the dodecagon is so round that it can almost roll like a wheel, as you can see in this Instagram video: For each of our regular polygons, let’s compute the ratio of the circumference to the diameter of its inscribed circle, and see how it compares to π≈3.14. What’s an inscribed circle, you might ask? That’s the largest round cookie you can make out of your polygon. Archimedes used both an inscribed circle and a circumscribed circle (the smallest circle that completely encloses the polygon) in his work on approximating π, but we’ll just stick to the former in this activity. You can do this activity with your students at two levels. For students who have not yet learned about special right triangles Measure the sides of the polygons and the diameter of the cookie cutter, then compute the ratio of the first quantity to the second. Let’s use the fact that the square is about 2.5 inches on the side. This is... read more
Geometry Installation by Hybycozo and Truncation

Geometry Installation by Hybycozo and Truncation

I was fortunate enough to visit downtown Los Angeles just in time to see this beautiful geometry installation by Hybycozo at the City National Plaza. The purple object on the left is an icosahedron, and the green one on the right — a truncated octahedron. The icosahedron is one of the 5 Platonic solids discovered several thousand years ago. Here is a picture of the Platonic solids from Johannes Kepler’s work,  Harmonices Mundi, in 1619:

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