## How to Guess the Day of the Week Your Friend Was Born

If you have some friends born between 1900 and 2000, then maybe you can impress them with this trick: find the day of the week that they were born.

Here are the steps:

(1) Let $y$ be the year of their birth. Evaluate $\frac{y - 1}{4}$ and ignore the remainder. For example, we want to know the date March 3, 1947, then we have

$\displaystyle \frac{1947 - 1}{4} = \frac{1946}{4} = 486$.

(2) Find what day of the year is the date and let’s represent it D. There are 31 days in January, 28 days in February, and March 3 is the third day.

$D = 31 + 28 + 3 = 62$

(3) Let $s = y$ + the result in (1) + $D$.

$s = 1947 + 486 + 62 = 2495$

4.) Divide $s$ by $7$ and get the remainder.

$\frac{2495}{7} = 356$ remainder $3$.

Now, you can guess the day of the week using the remainder.

Remainder: Day

0: Friday
1: Saturday
2: Sunday
3: Monday
4: Tuesday
5: Wednesday
6: Thursday

Hence, March 3, 1947 is a Monday.

Source: Nature of Mathematics

## Bach’s Music on a Moebius Strip

If you are fond of classical music, then you have probably heard of Johann Sebastian Bach. He was one of the great composers of the Baroque period. His music was known for its intellectual depth, technical command, and artistic beauty (I copied the last sentence from Wikipedia, lol).

But what will surprise you more is how his music is tied to mathematics. Watch the video below of how playing the music backwards and forwards simultaneously can be visualized using a Moebius Strip.

H/T: Open Culture

## The Beauty of Tessellations

Tiling is one of the many beautiful patterns that we can see around us. Some of them are man-made and some are created by nature. For example, many modern homes nowadays have tiled floors or even walls. On the other hand, in nature some animals are able to create regular tilings such as shown in the image below. Now why do bees would choose such shape?

Tiling, or popularly known as tessellation in mathematics, is not just beauty for the eyes. It has many interesting mathematical properties. For example, one question that should be asked what are the shapes that can tile a plane? What are the properties of these shapes? What are the properties of polygons that cannot tessellate the plane? Of course these questions had been answered hundreds or perhaps thousands of years ago, but they are a good exercise for the mind to those who haven’t encountered it. They are also good questions for students.  » Read more

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