MathematicsMaths is the subject where we never know what we are talking about,

nor whether what we are saying is true.--Bertrand Russel--

Math Humor• Two Physicists are in a hot air balloon. They’re theoretical physicists, so they

can’t read a map. As a result, they get lost. Helplessly drifting, they pass over a hill on which a man sits. They yell to him, “Hey, where are we?”

• The man sits and thinks about in he stands and thinks about it some more. He sits again, and thinks even longer. The physicists are just drifting out of earshot yells back to them, “You’re in a hot-air balloon!”

• Annoyed, one physicist turns to the other and says, “You know, I think that guy was a mathematician.”

• “How can you tell?”

• “Well, three reasons. First, he was absolutely right. Second, it took him a Long Time to get there.”

• “And third?”

• “And the third, It got us absolutely Nowhere!”

Essential Questions for Math

• What is mathematics about? (what is the raw material of mathematics?)

• What problems are solved by mathematicians?• How do the methods of mathematics generate

knowledge?• How can we analyse the certainty of claims in

mathematics?• What is special about the characteristics of math

compared to other areas of knowledge?

Scope & Applications: What is Math about?

OBJECTIVE: Explore Connections between Math & Nature: math as abstraction of patterns and concepts

• Exploring Patterns in Nature: Video Clip

• Activity-Collecting Samples from Nature

• Discussion

What is this?dried out river bed in desert

Bilateral & Radial Symmetry, circle, cone, hexagon, fractal, fibonacci sequence, golden

ratio, golden spiral

Fractal Patterns in Nature

Cone Shape in Nature

Video: Doodling in Math

• All of the images that preceded this slide represent common images in nature that occur over and over again & have mathematical properties

• Watch the video https://www.youtube.com/watch?v=ahXIMUkSXX0 by Vi Hart

Find, Discuss, Respond, & Share

• You have 25 min. for your group to find as many samples of the ideas discussed in the video outside on ISK campus

• Read pgs 355-356 in the Oxford Course Companion (Green text) Review the quote by Devlin (pg.356) and the questions in the box pg. 356 & discuss

• Jot down answers to the questions on a document you open on google drive and place in your TOK folder

• Based on what you’ve seen thus far, how would you define the subject of mathematics?