A Special Maths Day

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Key Stage 3 Maths By: Please log in to see tutor details
Subject: Maths » Key Stage 3 Maths
Last updated: 26/09/2016
Tags: dates, pythagoras theorem, square numbers

Last Sunday was a special day. Not only did we celebrate my daughter's birthday, it also was a special day in a mathematical sense. 25/9/16: three square numbers in a row. What's more, since 25 is equal to 9 + 16, the numbers satisfy the Pythagorean Theorem. Pythagoras’ theorem says that in a right-angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Let us now take a closer look at my daughter’s birthday date this year: 25/9/16. Because 25 = 9 + 16, we know that a right-angled triangle with sides 3, 4 and 5 exists. The hypotenuse has length 5, the other two sides length 3 and 4 respectively. The side lengths, 3, 4 and 5 form a Pythagorean triple and because 3, 4 and 5 are coprime, it is called a primitive Pythagorean triple.

Pythagoras’ theorem is used in more contexts than right-angled triangles. We encounter it in the equation of a circle, in the Euclidean distance between two points, the modulus of a complex number, and many more.

How many days like last Sunday do we have this year? In 2016 there have been 15 days with a date composed of three squares:

January: 1/1/16, 4/1/16, 9/1/16, 16/1/16, 25/1/16

April: 1/4/16, 4/4/16, 9/4/16, 16/4/16, 25/4/16

September: 1/9/16, 4/9/16, 9/9/16, 16/9/16, 25/9/16

Only one of the 15 triples satisfies that the sum of two of them is equal to the third, namely 25/9/16. In our 21st century, there are two days with this property: 25/9/16 and 16/9/25. My dear daughter’s birthday was a very special day indeed. 

Dr Katrien De Cock A-level Maths Tutor (South East London)

About The Author

I am a qualified Maths teacher, friendly, patient and committed. I work efficiently to get progress quickly.
I've always enjoyed doing mathematics and I love explaining it.

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