Please explain the Number Theory behind this trick :$latex boxed{frac {a } {b}= frac {frac {a}{b-a}}{frac {b}{b-a}}} &fg=aa0000&s=4$
Example: $latex 246 – 205 = 41$
$latex boxed {frac {205} {246}= frac {frac {205}{41}}{frac {246}{41}}=frac{5}{6}&fg=0000aa&s=3}$
…
Example:
27759 – 10227 = 17532 = 2 x 8766 = 2 x (2 x 4383) = 2 x 2 x (3 x 1461) = 2 x 2 x 3 x (3 x 487 )
$latex boxed {frac {10227} {27759}= frac {frac {10227}{1461}}{frac {27759}{1461}}=frac{7}{19}&fg=00aa00&s=3}$
Explanation:This method is from《九章算术》295AD 刘徽（曹魏/东晋），he invented the “Limit” 割圆法 method with 95-polygons to get the world’s best pi = 3.1416
https://zhidao.baidu.com/question/109475024.html
更相减损术证明：
Bézout’s Theorem :
For a, b CO-PRIME, ie gcd (a, b) = 1
There exist integersxandysuch thatax+by= 1
Historical Background:
Meek : 1/5 score = ‘Kiasu’ (怕输 )
Note: 林群院士是第一个把复杂吓人的
Two observations:
3. Category Theory = “Structural Relationship” Math
4. Algebraic Topology
Note: “Applied” Math vs “Pure” (aka Modern / Abstract) Math
2. Number Theory 史上第一本数论启蒙书：
Note:
Four Online Free Calculus Courses:
