Mystic Rose

Vertices	1	2	3	4	5	6
Lines
Regions

Aha! Just like so many other people you thought there would be 32 regions for the Mystic Rose with 6 vertices. Strange as it seems, the answer is not 32. Count again.

Check

Instructions

Use the drop-down box above to create Mystic Roses with different numbers of vertices. For each Rose you create count the number of vertex to vertex lines and count the number of regions the circle is divided into.

Complete the table above with your findings. Use the 'Check' button to ensure you are counting accurately. Can you see any patterns in the results?

You may be surprised to see that the number of regions in the six vertex Rose does not follow the pattern the previous Roses did. Have you any idea why? Leave a comment below if you have any thoughts.

If you are keen to investigate more you may like to consider the number of crossing points!

When you have completed the table you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

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Colour Choice

The following drop-down boxes allow you to customise the colours used in your Mystic Rose. The first box controls the lines joining each vertex to the adjactent vertices. The second drop-down controls the lines connecting every second vertex and so on.

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Transum,

Monday, April 20, 2015

"When considering the number of regions for the six-vertex rose it is worthwhile to draw the rose using compasses, marking of the six equally spaced points using the compasses still at the same radius then colour in the regions using only two colours and seeing the connection with the Two Colour Theorem for colouring maps.

When that is complete an extension activity could be identifying all of the shapes that can be found in the six-vertex Mystic Rose. The list will include rhombus, kite, segment, sector and many more."

@MissingPercent1, Twitter

Tuesday, November 28, 2023

A Desmos file for anyone that would like to make hypocycloids:

Use lines 34 and 59 to change colours or remove shading.

Please let me know if you find any mistakes or have any suggestions. #mathart https://t.co/A6RDe8GWXt pic.twitter.com/mp8bnE3sCN
— The Mystery of the Missing Percentage Sign (@MissingPercent1) November 26, 2023

Printable sheets of Mystic Roses are available for use in the classroom. The first two pages have the first 12 Mystic Roses and the third page has multiple copies of the six-vertex Mystic Rose. The latter has been used successfully in shape finding investigations eg. "How many different shapes can be found in the six-vertex Mystic Rose? Can you mark the parallel sides, equal angles etc.

Other shape counting starters:

Information

From Wilipedia:

"In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. Drawings of complete graphs, with their vertices placed on the points of a regular polygon, appeared in the 13th century, in the work of Ramon Llull. Such a drawing is sometimes referred to as a mystic rose."

This interactive page provides a starting point for your investigation of Mystic Roses. Is there a pattern in the number of chords, regions or chord crossing points for the sequences of Roses with more and more vertices?