3.7 Similarity
Ratios and Proportions
I.SectionObjectives
- Write and simplify ratios.
- Formulate proportions.
- Use ratios and proportions in problem solving.
II.Cross-curricular-GreekArchitecture
- Provide students with an image of the Parthenon from Wikipedia.
- This is Figure 08.01.01
- http://www.en.wikipedia.org/wiki/File:Parthenon-2008.jpg
- Then provide students with an image of the Acropolis from Wikipedia.
- http://www.en.wikipedia.org/wiki/File:AthensAcropolisDawnAdj06028.jpg
- Now use the images as a discussion about the golden ratio of approx. 1.6 and how this is shown in the
dimensions of each building.
III.TechnologyIntegration
- Students can look at this website using The Golden Ratio and talking about how beauty has to do with ratios.
Check it out first. - http://www.intmath.com/Numbers/mathOfBeauty.php
- Students can also use this website which looks at ratios in nature.
- http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html
- This website has a ton of different links for students to explore when looking at how ratios play into different
topics.
IV.NotesonAssessment
- The content of this lesson is assessed through the discussion.
- You want students to understand that when you compare different facets, the ratios impact the design.
- With the golden ratio, the ratio is the same.
- Then you want the students to begin to make the connections on their own.
- Students can see the real life examples of ratios, especially the golden ratio.
Properties of Proportions
I.SectionObjectives
- Prove theorems about proportions.
3.7. Similarity