Maths History
Ramanujan and number patterns
Introduce a mathematician famous for extraordinary number insights.
Quick answer
Ramanujan was a brilliant Indian mathematician who discovered amazing number patterns and secrets in maths, even though he had very little formal training.Learning outcome
By the end of this page, you will understand how Ramanujan found special number patterns and how you can discover your own patterns too.Why this matters
Ramanujan showed us that maths isn’t just about numbers and calculations – it’s also about finding surprising connections and secrets. His work helps us understand how numbers can behave in unusual ways, and it shows that anyone, no matter how young or how little they’ve studied, can find interesting patterns in maths.How it works
Ramanujan was born in 1887 in India and loved playing with numbers. He didn’t go to school for maths, but he discovered patterns in numbers that experts only found much later. Here’s how he did it: 1. He looked closely at numbers. Ramanujan noticed that numbers could be grouped in special ways. 2. He saw patterns in repeated addition or multiplication. He found that some numbers were related in surprising ways. 3. He trusted his instincts. Even when others didn’t understand his ideas, he believed in them and kept exploring. 4. He shared his discoveries. He wrote letters to famous mathematicians, sharing his findings.Examples you can see
Let’s imagine Ramanujan is in a garden with flowers. He sees that there are 3 rows of flowers, and each row has 4 flowers. So he counts: - 4 flowers in the first row - 4 flowers in the second row - 4 flowers in the third row This is like 3 groups of 4, or 3 × 4 = 12 flowers. Now, let’s try a trick that Ramanujan might have used. Imagine you have a row of 5 numbers: - 1, 2, 3, 4, 5 If you add them all up, you get: 1 + 2 + 3 + 4 + 5 = 15 Ramanujan would have noticed that this is the same as: 5 × 6 ÷ 2 = 15 This is a pattern that works for any group of numbers in a row. If you have 10 numbers: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55 And: 10 × 11 ÷ 2 = 55 This is one of the patterns Ramanujan discovered – and it helps us add numbers quickly. Let’s try another pattern with squares. Look at this: - 1² = 1 - 2² = 4 - 3² = 9 - 4² = 16 - 5² = 25 Ramanujan noticed that the differences between these squares follow a pattern too: - 4 – 1 = 3 - 9 – 4 = 5 - 16 – 9 = 7 - 25 – 16 = 9 So the differences are 3, 5, 7, 9 – these are odd numbers that go up by 2 each time.Try it as a mini adventure
Let’s go on a pattern-finding mission! Adventure: The Number Pattern Hunt You are a young mathematician like Ramanujan. You are in a magical garden where numbers grow like flowers. Each flower has a number on it. 1st flower: 1 2nd flower: 3 3rd flower: 6 4th flower: 10 5th flower: 15 Can you see the pattern? What number will be on the 6th flower? Hint: Try adding the number of flowers you’ve seen so far. - 1st flower = 1 - 2nd flower = 1 + 2 = 3 - 3rd flower = 3 + 3 = 6 - 4th flower = 6 + 4 = 10 - 5th flower = 10 + 5 = 15 - 6th flower = 15 + 6 = 21 So the 6th flower has the number 21. Now try this: What number will be on the 7th flower? - 7th flower = 21 + 7 = 28 You’ve found a special pattern – these are called triangular numbers.Common mistakes
- Mistake: Thinking that all patterns are about multiplication tables. Why it happens: Children often only see numbers in rows like 2, 4, 6, 8 and think that’s all patterns are. Fix: Show that patterns can be about addition, subtraction, or even the way shapes grow.
- Mistake: Believing that Ramanujan’s discoveries were too hard for children to understand. Why it happens: Adults sometimes think that only experts can find deep maths. Fix: Remind children that even simple patterns can lead to big discoveries.
- Mistake: Counting backwards or skipping numbers in a pattern. Why it happens: Children can get confused when numbers are not in order. Fix: Use visual aids like counters or drawings to help track each step.
Parent and carer guide
As a parent or carer, you can help your child by: - Playing pattern games together, like counting how many tiles are in a row or how many steps you take. - Looking for patterns in everyday life – like how many eggs are in a carton (6 eggs in 1 row), or how many fingers on 3 hands (15 fingers). - Encouraging curiosity – ask questions like “What do you notice about these numbers?” or “Can you find another way to group them?” - Reading stories about famous mathematicians like Ramanujan to show that maths can be creative and fun. - Not worrying about the answers – it’s more important to explore and think than to get it right the first time.Practice questions
- What is the next number in this pattern: 2, 4, 8, 16, ?
- What is the sum of 1 + 2 + 3 + 4 + 5?
- What is the 5th triangular number?
- What is the difference between 6² and 5²?
- How many flowers are there in 4 rows of 5 flowers each?
- 32 (Each number is doubled)
- 15
- 15 (1 + 2 + 3 + 4 + 5)
- 11 (36 - 25)
- 20 flowers
FAQ
Who was Ramanujan?
Ramanujan was a brilliant Indian mathematician who made important discoveries in number theory and infinite series, even though he had no formal training.
What is a number pattern?
A number pattern is a sequence of numbers that follow a rule or a special way of growing, like adding 2 each time or multiplying by 3.
Can children find number patterns too?
Yes! Anyone can find number patterns. Ramanujan started by looking closely at numbers and asking questions.
What are triangular numbers?
Triangular numbers are numbers that can form a triangle. For example, 1, 3, 6, 10, 15 are triangular numbers because they can be arranged in triangles.
Why are number patterns important?
Number patterns help us understand how numbers work, solve problems, and even predict what comes next in a sequence.