Nature's Favourite Sequence Visual
Daisies and beat structures provide concrete connections to the abstract numbers.
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The number of petals on many flowers, like daisies, naturally follow the Virahāṅka sequence.
Students will generate the Virahanka-Fibonacci sequence and apply it to combinatorics problems.
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Introduce the poetry beat problem.
Thousands of years ago, Sanskrit and Prakrit linguists studied the rhythm of poetry. They classified every syllable in a poem as either short or long.
Daisies and beat structures provide concrete connections to the abstract numbers.
The number of petals on many flowers, like daisies, naturally follow the Virahāṅka sequence.
Define the Virahanka sequence logic.
How do we find out the number of combinations without listing them all manually? The answer lies in the Virahāṅka sequence.
Every 5-beat rhythm must begin with either a 1-beat (short) or a 2-beat (long) syllable.
Daisies and historical context.
The Indian scholar Virahāṅka discovered this sequence around 700 CE while studying poetry, predating the Italian mathematician Fibonacci by about 500 years!
These exact numbers () appear naturally in the petals of daisies. Mathematics is woven right into the fabric of nature!
Worked example showing how the previous two terms sum to the next.
Problem. You want to find the number of different ways to write the number as a sum of s and s (representing 5 beats of short and long syllables).
You already know that there are ways to make a 4-beat rhythm, and ways to make a 3-beat rhythm.
Faded example for n=6.
To find the number of ways to create a 6-beat rhythm, we use the rule discovered by Virahāṅka. First, we need to know the number of -beat rhythms, which is . Next, we find the number of 4-beat rhythms, which is . By adding these two previous terms together, we find there are exactly rhythms having 6 beats.
Identify the odd/even pattern in the sequence.
What is the repeating parity pattern of the numbers in the Virahāṅka sequence ()?