Bringing in Autumn with Spread of Math Delicacies

Welcome to the 175’s edition of Playful Math Carnival, and if it’s your first visit to my site, welcome to the Beauty of Play. The Playful Math Carnival is a monthly collection of math fun: tips, games, activities and more. Denise Gaskin’s from Let’s Play Math founded the series. Each month, she finds different blogs to host the carnival. For the month of September, that’s me!

In this edition you’ll find:

Let’s start by celebrating the number 175.

• 175 ends in 5, so it is a composite number, not a prime. Its factors include 1, 5, 7, 25, 35, and 175. If we were to factor it by color using Prime Climb, we would have two blues and one purple.
• A perfect number is a number whose factors, not including the number itself, add to that number. 175’s factors add to 73. This means the number is not perfect, but deficient because the sum of the factors is less than the number itself. If the sum of the factors were more than 175, the number would be abundant

1 + 5 + 7 + 25 + 35 = 73

• What about happy? Is 175 a happy number? Happy numbers are numbers whose sum of the digits squared repeated until a single digit is acheived eventually give one. We see from the sums of the squares below, 175 is sadly not a happy number.

1² + 7² + 5² = 1 + 49 + 25 = 75
7² + 5² = 49 + 25 = 74
7² + 4²  = 49 + 16 = 65
6² + 5²  = 36 + 25 = 61
6² + 1²  = 36 + 1 = 37
3² + 7²  = 9 + 49 = 58
5² + 8²  = 25 + 64 = 89
8² + 9²  = 64 + 81 = 145
1² + 4² + 5²  = 1+ 16 + 25 = 42
4² + 2²  = 16 + 4 = 20
2² + 0²  = 4 + 0 = 4

-Not Happy

• It is the difference between two consecutive fourth powers. 4⁴ – 3⁴  
• 175’s binomial expressions is 10101111, making it ‘evil,’ not odious because of the even number of 1’s.
• Expressed as a Roman numeral it is CLXXV.
• 175 and its square, 30,625, as well as its cube, 5,359,375 both end in 5.
• To count to 175 would take roughly twenty-eight seconds.
• It is not in the Fibonacci sequence, not a triangular number, and not a square or a cube number.
• Its square root is 13.228756555323.

A Game

I’m copying a game that I really enjoyed playing from Denise’s 171 edition. This game has to do with palindrone numbers. To play, add the number and its reverse, and continue doing so with the result until you come to a palindrome number. Color code the number of steps on the 100 chart.

One of the reasons that I love this so very much is that it has a pattern of colors it makes on a 100 chart. Can you guess what that pattern is? Here’s a free blank 100-chart to record your findings.

Physical Construction of the Hyperboloids

In this post, Skewer Hyperboloids, mathematical artist and retired engineering professor, George Hart leads a group of middle schoolers through the physical construction of a hyperboloid using skewers and rubber bands. He gives instructions on how to make your own. George also has his own YouTube channel and together with Elisabeth Heathfield created Making Math Visible. Interestingly enough, Mr. Hart is the father of the YouTube creator ViHart. If you haven’t seen her channel, it’s worth checking out.

Folding the Circle

Continuing with the Geometry theme, author and sculpture, Bradford Hansen-Smith, takes us through a lovely exploration of bringing two-dimensional circles into both simple and elaborate three-dimensional shapes in his Whole Movement: Folding the Circle for Information. This is the epitome of the Quality of Numbers from Waldorf pedagogy. These are beautiful pieces of mathematical art that they have made a curriculum for. You can view this three-volume series through their shop: Red Hen Toys.

Progression of Roots

Moving on to the beautiful display of the Progression of Roots, also called Spiral of Theodorus. This series of rectangles whose side is the previous rectangle’s diagonal, beginning with the first rectangle as a square (side unit of 1) leads us through a progression of right triangles whose diagonols measure a series of the square roots of natural numbers beginning with the square root of 2.

This would be the perfect construction to do a Notice and Wonder. If you aren’t familiar with ‘notice and wonder,’ you can find a blog post of where we used notice and wonder here.

It’s also just a beautiful display of math. Amplify has a lesson plan where they take the triangles with the hypotenuses of the progressive radicals and place them on a number line, estimating the measurement of each radical. They also use Mathigon, a virtual “mathematical playground” to construct the progression.

Prime and Composite Dot Animation

The last thing I’ll leave you with today is an animation of patterns of prime and composite numbers on a blog post called, Dance, Factors, Dance. It’s such an apt name for this interactive “a promenade of primes (and) composites.” You can find that interactive animation HERE. This is another opportunity to use ‘notice and wonder’ and PLAY with math.

This animation is from Stephen Von Worley, whose page, Data Pointed has a collection of his data visualization research on topics of things you would not expect. Some of the most interesting to me, aside from this animation, are the Color Strata visuals which shows a visual of a color name survey and The Skies are not Cloudy All Day where he has a visual of the total distance of one famous fast food restaurant in the US to another.

Closing

I hope you have enjoyed this edition of the Playful Math Carnival hosted by Denise Gaskins, the author of Let’s Play Math. Previous Carnival’s include:

Playful Math Carnival #174 by Math Mama Writes
Playful Math Carnival #173 by Nature Study Australia
Playful Math Carnival #172 by Let’s Play Math
Playful Math Carnival #171 by Let’s Play Math

Next month, my friend Sonya from Learning Well at Home is hosting.

Until next time.