Flower Power

8866 /www/nrich/html/content/id/8866/ 1 0000-00-00T00:00:00 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <ul id="stemLinks"> <li><a href="http://nrich.maths.org/8393">Warm-up</a></li> <li><a href="http://nrich.maths.org/4855">Try this next</a></li> <li><a href="http://nrich.maths.org/4972">Think higher</a></li> <li><a href="http://nrich.maths.org/8194">Read: mathematics</a></li> <li><a href="http://www.exploratorium.edu/snacks/moire_patterns/index.html">Read: d</a><a href="http://plus.maths.org/content/power-origami">esign</a></li> <li><a href="http://motivate.maths.org/content/smart/LogoStars">Explore further</a></li> </ul> <div> </div> Imagine you are a fabric designer. This is your brief: <mdo:image alt="flower design" src="FlowerPower.png" style="width: 250px; height: 250px; float: right; margin: 25px;"></mdo:image> <div class="framework" font="" size="+1">Create a design for a patterned fabric based on a flower motif. The motif should show rotational symmetry. The motif should be repeated across the width and length of the fabric in an interesting way which also shows symmetry. Start by roughing out a design. You may wish to use a real flower for inspiration, or you could start from something more abstract provided it can be recognised as a flower. When you are happy with your design, use Logo to create a print of the fabric. If you wish to submit your design, include a screenshot and the Logo program you used to create it, together with a summary of the symmetry shown by the motif and by the overall design.</div> Ideas to think about: <ul> <li>The number of petals of many flowers is given by the <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html#petals">Fibonacci sequence</a>.</li> <li>What calculation do you need to do to work out the angle between petals if the flower is to show rotational symmetry?</li> </ul> If you would like help in getting going with Logo, <a href="http://nrich.maths.org/8045">these graded problems</a> will help you. Windows users can download a free copy of Logo from <a href="http://fmslogo.sourceforge.net/">FMSlogo.</a> A good free version for Mac users is <a href="http://www.alancsmith.co.uk/logo/">ACSlogo</a>. There's a version you can run directly in your browser at <a href="http://calormen.com/logo/">http://calormen.com/logo/.</a></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">It is not envisaged that <a href="http://nrich.maths.org/8866">this problem</a> would be used as a class problem. It is more appropriate for an enthusiastic student or small group of students looking for a challenge to work on independently. Students who want help in getting going with Logo could try some of the problems in <a href="https://nrich.maths.org/8045">Fast Forward Into Logo</a> or <a href="http://nrich.maths.org/8393">Making Moire Patterns</a>.</mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><mdo:image alt="Logo flower design" src="FlowerPower2.png" style="width: 250px; height: 250px; margin: 10px; float: right;"></mdo:image>This is the program I used for the basic design in the image. You could copy it and adapt it if you wish (you may not need 'To' or 'end', this will depend on which version of Logo you are using). The program consists of four Logo Procedures: <div style="margin-left: 40px;">To petal ht lt 40 repeat 16[fd 4 rt 5] rt 100 repeat 16[fd 4 rt 5] rt 140 end To flower repeat 5[petal rt 72] end To strip repeat 5[flower pu fd 128 pd] end To fabric pu lt 90 fd 300 rt 90 bk 300 pd repeat 5[strip pu rt 90 fd 120 lt 90 bk 560 pd] end </div> <div>Logo commands</div> <div class="toggle">ht = hide turtle lt - left fd = forward rt = right pu = pen up pd = pen down bk = back</div> <div style="margin-left: 40px;"> </div> <div> Can you see what each program and each command is doing? The forward distance of 4 pixels was chosen to give a sensible size of petal. What happens if you change it? Similarly the angle change of 5 degrees seemed to give a good result. What happens if you change this? And how do you have to change the other angles and the number of repeats if you change it? The forward and backward instructions in To fabric at the beginning and at the end of the repeat were chosen fairly arbitrarily to give an effective design. </div> <h4>Generalising the program</h4> You can generalise the petal size and hence the size of the finished design by using a variable instead of the length of 4. See if you can work out how to do this: <a href="http://nrich.maths.org/4855">help in using variables</a>. Can you then generalise for the number of petals in the flower? </mdoxml> 2 3 0 0 1 1 0 Flower Power Create a symmetrical fabric design based on a flower motif - and realise it in Logo. Applications STEM - living world Applications Design Applications textiles Admin Featured STEM Applications STEM - design technology Information and Communications Technology Logo Information and Communications Technology Programming Transformations and their Properties Symmetry