Compare and contrast the IB Math guide and the IB TOK Math section.
Note and discuss similarities and differences before looking at this document.
In TOK we will focus on :
how mathematical knowledge is created rather than understanding complex mathematical knowledge.
Certainty of mathematical knowledge rather than creating or proving mathematical theorems.
Understanding the benefits and limitations of logical arguments rather than creating/evaluating logical arguments.
2. What do mathematicians do all day? Note down ideas before watching///
Pure & Recreational Mathematics
3. Watch the Between the folds trailer then explore The fold and cut problem for yourself.
What's the point of this?
The point?
While the Fold-and-Cut Problem may seem like just a recreational mathematical puzzle, it has several practical applications. For example:
Origami: Origami artists use folding techniques to create intricate designs, and the Fold-and-Cut Problem provides a way to create more complex shapes.
Manufacturing: The Fold-and-Cut Problem has applications in the manufacturing industry, such as in the design of folded structures or the creation of packaging materials.
Biology: The Fold-and-Cut Problem has also been used to model the folding of biological molecules, such as proteins.
Computational Geometry: The Fold-and-Cut Problem is a classic problem in computational geometry, and has been studied extensively as a test case for computational algorithms and geometric constructions.
In summary, the Fold-and-Cut Problem has a wide range of applications in various fields, making it an interesting and relevant problem for mathematicians, computer scientists, and engineers alike.
Reveal....
“A Fractal is a type of mathematical shape that are infinitely complex. In essence, a Fractal is a pattern that repeats forever, and every part of the Fractal, regardless of how zoomed in, or zoomed out you are, it looks very similar to the whole image.”
Applications of fractals include - more accurate representations of coastlines, clouds, cities, lungs and biomimicry (mimicking nature to solve human problems) to name a few. - recreate and make models using mathematics, which can be easier analyzed uses today
Click here for more examples
5. Explore other dimensions - (5 min video) Consider why exploring other dimensions might have value while watching.
6. Open problems in mathematics are another aspect to consider in relation to the scope. Where's the value in open problems such as those presented by the Clay institute or pure mathematics such as complex numbers or Fermat’s Last Theorem?