Interesting Numbers To Show Your Class
In this blog we cover five interesting sequences of numbers to show your class. They are outside the scope of the curriculum, and will be a great way to ignite the curiosity of your pupils.
There is a brief introduction to each sequence, and hopefully this article will be a springboard for further investigation, by teachers and pupils alike.
Tetrahedral Numbers
![Tetrahedral Number in Java](data:image/png;base64,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)
Image Credit: JavaTpoint - Tetrahedral Number in Java
Your pupils might be able to remember what a triangular number is. Tetrahedral Numbers are made by adding up their more famous cousins, the triangular numbers. (Triangular Numbers are: 1,3,6,10,…)
To work out the fourth Tetrahedral Number, add up the first four Triangular Numbers.
The 4th Tetrahedral Number 1+3+6+10=20.
As you can see from the picture above, tetrahedral numbers look like tetrahedrons when they are arranged in the right way. Tetrahedral numbers have real world applications in Sphere Packing, which is the science of packing spheres (often applied to molecules) in the most efficient way possible.
Perfect Numbers
![](data:image/png;base64,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)
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A Perfect Number is equal to the sum of its proper factors. Proper factors mean that you aren’t including the number itself.
6 is the smallest Perfect Number: 6=1+2+3
Question to ask: Can your pupils find the next Perfect Number less than 30?
Below is a list of the first 10 Perfect Numbers. The 10th Perfect Number is absolutely huge. It is in fact an unsolved problem in mathematics as to whether there are infinitely many perfect numbers. It is really good for pupils to find out that mathematicians don’t know everything.
First ten Perfect Numbers: 6, 28, 496, 8128, 33550336, 8589869056, 137438691328, 2305843008139952128, 2658455991569831744654692615953842176, 191561942608236107294793378084303638130997321548169216
Perfect Numbers don’t however just appear randomly, there is a fascinating connection between Perfect numbers and Mersenne Primes as can be seen in Numberphile's Perfect Numbers and Mersenne Primes video. It only gets better – All Perfect Numbers are themselves Triangular Numbers as well!
Related to the concept of Perfect Numbers, are the ideas of Abundancy and Deficiency. As you might be able to guess, If the proper factors add up to less than the number, it is deficient. If they add up to more than the number, it is abundant. Choose some (reasonably sized) numbers for your pupils to classify as abundant, deficient or perfect.
Lazy Caterer’s Sequence
Imagine you have a round pizza and you are going to make straight cuts at random. What is the maximum number of pieces you could divide your pizza up into? For one cut it is two pieces. For two cuts, it is also easy, it is four pieces. For three cuts it is a bit harder, but with some work we can see it is seven pieces.
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)
Image Credit: Wikipedia - Lazy caterer's sequence
With three cuts the maximum number of pieces is seven.
We are starting to form a sequence: 1,2,4,7,… It starts with the number 1, because we want to show what will happen with zero cuts. Ask your pupils to try and generate the next number in the sequence.
![](data:image/png;base64,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)
Image Credit: Wikipedia - Lazy caterer's sequence
The Lazy Caterer’s Sequence [1,2,4,7,11,16,…] is a very interesting sequence. It has a quadratic nth term, and the sequence can also be found inside Pascal’s Triangle. (Can you spot it?)
Keith Numbers
Keith Numbers are relatively young, having only been ‘discovered’ by Mike Keith in 1987. They are part of what is called Recreational Mathematics, which is the art of doing mathematics just for fun.
How to decide if your number is a Keith Number:
Let’s test the number 197
Step 1. Decide how many digits your number has. For 197, n=3, where n is the number of digits.
Step 2. Add up the digits of your number. 1+9+7 = 17
Step 3. Add up the last n=3 numbers in the sum above. 9+7+17 = 33
Step 4. Repeat this process to see if your original number appears. (If the original number never appears it is not a Keith Number.)
7+17+33 = 57
17+33+57= 107
33+57+107 = 197 [Hooray, we found 197, the original number – 197 is a Keith Number!!!]
How it works for a two-digit number:
Let’s test the number 19
Step 1. Decide how many digits your number has. For 19, n=2, where n is the number of digits.
Step 2. Add up the digits of your number. 1+9 = 10
Step 3. Add up the last n=2 numbers in the sum above. 9+10 = 19
[We found 19, the original number – 19 is a Keith Number!!!]
There is no known purpose to Keith Numbers apart from the sheer mathematical pleasure that they give. History has however proved time and time again that recreational mathematics can lead to unexpected breakthroughs further down the line.
Check out the Numberphile Video on Keith Numbers.
Look and Say Sequence
The following sequence is one of the most bizarre that you will ever meet. If you have not encountered it before, take a few minutes to see if you can work out what the pattern is.
1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, …
Read below for the answer………..
What you need to do is to read it out loud – i.e. ‘Look and Say’ what you see.
The sequence starts with the number 1.
Say “One one.” Write down 11.
Say “Two ones.” Write down 21
Say “One two, one one.” Write down 1211
Say “One one, one two, two ones.” Write down 111221
And so on…..
Is the Look and Say Sequence Mathematical Nonsense?
This sequence may look like mathematical nonsense, but your pupils will enjoy generating the next few terms of the sequence and some of them might even like to take their sequence home as a party trick to show their families.
When this sequence was shown to John Horton Conway, one of the greatest mathematicians of the 20th Century, he couldn’t resist getting his teeth stuck into it, and went on to show that it has some fascinating mathematical properties.
Amongst other things, John Conway started taking two consecutive terms and working out the ratio between how many digits they have.
For example, take the 7th and 8th terms: 13112221 (has 8 digits), 1113213211 (has 10 digits). John Conway was looking at the ratio: 10/8 = 1.25. If you keep doing this for consecutive pairs of numbers, as they get really large, the ratio will tend towards 1.303577… which is now known as Conway’s Constant. This sequence proves that mathematics really is everywhere.
John Horton Conway talks about Look-and-Say Numbers on a Numberphile video.
Make up your own sequence
One idea is for pupils to make up their own sequence of numbers and to give it a name. What do they come up with and can they spot any patterns?
Further Reading
If you’ve enjoyed this article, why not take a look at our article on the Five Fascinating Mathematical Objects That Your Pupils Need To See!
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