You will create a poster of the Pythagorean spiral. The result needs to be colored and may be creatively decorated based on the image you choose to emulate. You will need to turn in your poster, a separate piece of paper with all calculations, a three paragraph (>120 words) summary of the creature you studied and the photo you worked to duplicate.
Materials: standard (22×28) poster board + ruler + protractor + pencil, colored pencils or markers
Basic overview (you do NOT have to follow exactly)
Step 1: Place the poster board in landscape orientation. Measure from the top left hand corner 27.5 cm right and 20.5 cm down. This will be the starting point for your diagram. It will assure that your diagram stays on the page.
Step 2: Using your ruler create a segment that is 10 cm across starting from the starting point and heading towards the center of the poster. Make this segment perpendicular to the side of the poster. Use your compass and ruler (without measuring) to construct a congruent segment that is perpendicular to the original. Connect the endpoints of the two segments to create a right isosceles triangle.
Step 3: On a separate piece of paper, use the Pythagorean Theorem to calculate the length of the hypotenuse. Show all work and write your answer in reduced radical form.
Step 4: Using the hypotenuse of the first triangle, create another right triangle on top of the previous hypotenuse. The old hypotenuse will be the new base and construct a perpendicular segment to this, with a length of 10. Then connect the two segments to form a new hypotenuse. Use your protractor to be certain the new edge is perpendicular to the old hypotenuse i.e. 90 degree angles. Each new perpendicular edge must measure exactly 10 cm.
Step 5: On your separate piece of paper, show the calculations to find the length of the new hypotenuse. As you develop your calculations for each right triangle, notice the pattern of how the hypotenuse grows. Simplify your radicals by factoring. DO NOT USE DECIMALS ! !
Step 6: Continue to repeat this process of connecting and constructing new triangles with a side length of 10, using the previous hypotenuse as the other side. Continue to show your calculations on your separate piece of paper. Construct triangles until you have formed a full spiral. If your calculations and drawings are correct, your 1st, 6th and 17th triangles should end (approximately) on the same line where you began. It may take a while to perfect .
Step 7: Go to Google or Bing Images and search through pictures that come up with “Chambered Nautilus”, “Snail Shell” and “Ram’s Horn”. Try to think of any other creature where this pattern is displayed. Be creative and persistent in your quest to find a unique representation. Select a creature that appeals to you and print out a copy of the image. You will turn your Pythagorean spiral into a replica of the image you selected, thereby creating a Pythagorean Creature Feature! Use colored pencils or markers to alter/adjust/design/color the spiral until it is a close approximation of the picture you printed.
Reference: https://www.oercommons.org/courseware/lesson/64439/overview
Step 8: Type a three paragraph summary of this process. The first paragraph (> 120 words) will be on what you learned mathematically. The second paragraph (> 120 words) focuses on what you learned about the creature and how their spiraling part is formed. The third paragraph (>120 words) will present your views on how nature could produce a spiral so perfect that you were challenged to reproduce it by hand with a protractor and calculator. Please use a proofreader, or at least the spell check feature in Windows, before submitting.
Completion Dates:
PCF#1 Steps 1 – 6 – Calculations page needs to be finished by Friday, May 17th.
PCF#2 Step 7 – Rough draft (black and white) is done by Thursday, May 23rd.
PCF#3 Step 7 – 8 – The finished Pythagorean Creature artwork (color) and typed summary is due on Tuesday, June 4th. ON THE BACK OF THE POSTER: the calculations to the upper right. (3) the rough draft on the top left corner and a copy of this assignment in the bottom right corner. Your Parent Approval statement and signature go in the middle and the graded rubric on the bottom left corner. ON THE FRONT put your name, class and date on the bottom right and a copy of the photo on the bottom left and staple the typed summary to the upper left corner.
We will practice the calculations and design several times in class prior to the due dates.
he goal of the project is to help students recognize the mathematics that is all around them….in nature. The Calculations Sheets and Rubrics have been distributed and students will need to select a natural creature/phenomenon to demonstrate this expanding curve.
