The 3 ancient Greek Problems are:
1. Trisect a Triangle
2. Square a circle
3. Doubling a Cube
Why restrict using only unmarked ruler ?
Answer: Using a Straight line:
Why a compass?
Answer: Using a Circle:
The Greek 3 Problems have been proven by 19th Century impossible to solve with only a straight line and a circle.
China, Singapore, Hong Kong and Taiwan are 4 predominantly Chinese population being ranked 1st, 2nd, 3rd and 4th, respectively, in the PISA 2012 Math Test for 15-year-old students.
While this is something to be proud of our Secondary School Math Education, it does not hide the fact that beyond this age (15) these countries do not produce any high-level mathematicians like Fields Medalists or Nobel Prize Scientists.
What goes wrong ?
Reason: Asian education emphasizes on computation-driven Math drills, a long tradition of ‘abacus’ mindset, or ‘algorithmic‘ approach.
By doing plenty of Math assessments : in China “Sea of Math Questions” (题海), or in Singapore popular Math Tuition Class doing Past Years Math Papers, students are drilled in solving standard ‘sure-have-answer’ test questions with memorized or déjà-vu (of similar patterns) problem solving techniques.
Once they enter university where the Math is more of Proofing and “no-solution” type, most students are not trained in thinking and solving such questions, they will get stuck.
What Asian Math Education should improve is in the “Solving Unknown” Math skills – something worth to learn from the French Lycée (Secondary /High School) Math Education since they incubate 1/3 of Fields Medalists, yet France’s PISA is average. (Why ? – another blog to discuss the French’s weakness in Applied Math.)
We learn Discrete Math in Integer (discrete means increment by 1: n, n+1, (n+1)+1…), then we struggle with the epsilon-delta to find limit, continuity… in Analysis.
Discrete is Macro Math, Analysis is Micro Math. Now Terrence finds a bridge between them: Ultraproduct.
is almost a whole number !
is the last one of the list d which allows unique prime factorization in Z[d].
Why not in d?
6 = 2 x 3
Answer : 16
D. Knuth “Digital Typography”