创办美国最大的在线数学社区AoPS.com

【创办美国最大的在线数学社区,他一针见血指出了数学学习的关键所在】
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https://artofproblemsolving.com/

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Relativistic Space Time, Fengshui, Isometry

风水 Fengshui (aka Geomancy) is Einstein Relativistic using Compass (东西南北上下 =Space) & Timing (吉凶日/时间 = auspicious date & time).

\Yu (Space) \Zhou (Time) = Space-Time
eg.
宇环 (universal surrounding)
宙时 (instant timing)

https://www.asiatimes.com/2019/08/opinion/why-quantum-physics-needs-asian-philosophy/

Axonometry = Isometry ( dengjiao toushi 等角透视,ie Angle Preserved Projection )

Chinese art is axonometric using isometry geometry, scrolling from right to left along time. Example : this digital animated 12-century painting

清明上河图 Qingming Festival River Scene(北宋)

“Why the world relies on a Chinese ‘perspective’” by Jan Krikke, China, AI and Quantum Physics

https://link.medium.com/z5LaoL0tdZ

China Gaokao 2019 Interesting Math Question

Gaokao = Baccalaureate = GCE A Level

…[Solution scrolled below]

Let Ф = 0.618

… Golden Ratio Ф = 0.618

defined as:

“Head to Throat” vs “Throat to Navel” = a/b = Ф ,

also

“Head to Navel” vs “Navel to bottom of Legs” =(a+b) / c= Ф

Knowing :

Head to Neck = 26 cm &

Legs = 105 cm

Find the height (H) ?

Note: The tricky part is to know “the neck is below the throat” & “the legs start some distance below the navel”, hence 2 inequalities :

a < 26, c > 105

H = (a + b) + c = Фc + c = (1+Ф) c = 1.618c
H > 1.618 x105
H > 169.9

H = a + b + (c)
= a + b + (a+b) / Ф
= (a+b) (1+1/Ф)
= (a +a/Ф) (1+1/Ф)
= a(1+1/Ф)(1+1/Ф)
< 26.(1+1/Ф)(1+1/Ф)

H < 178.2

ANS = H ~ 175 (B)

苏联数学三巨头之 Gelfand 盖尔范德

【苏联数学三巨头之盖尔范德】自修成才

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5G Concert by Players Worldwide

这就是5G的厉害:The Power of 5G

六国音乐家在六地通过5G网络,合奏巴赫C小调前奏曲与赋格。6 countries play over 5G simultaneously with no transmission latency.

第一小提琴德国,Violin 1 (Germany)
第二小提琴西班牙,Violin 2 (Spain)
第三中提琴蒙古,Viola (Mongolia)
第四大提琴瑞典,Cello (Sweden)
第五钢琴美国, Piano (USA)
第六定音鼓日本, Timpani (Japan)

他们在世界各地,声音同步传输,没有任何延迟!

Different Views of Category, Type & Set

Different views of objects 对象 by:

1. Category 范畴 “Cat” (morphism* between Objects, Functors ‘F‘ between Cats);

2. Set 集合 (a “smaller Cat”, only objects);

3. Type 类型 (deal only with same kind of objects: Int, String, Boulean…).

Note : Category can be a Set (SET) , Group, Ring, Vector Space (Vect) , “Topo” (Topology) … any algebraic structure with Associative Morphism (Map or ‘Arrow’ ) between them.

Note (*) : A morphism 态 in layman’s term is best illustrated by geometry:

2 triangle objects are similar 相似 = homomorphism 同态

2 triangle objects are congruent = isomorphism 同构

https://www.quora.com/share/Whats-the-difference-between-category-theory-and-type-theory-1?ch=3&share=2af1c06a

Note: Analogy –
Category : School
Type : Boy Class, Girl Class
Set : Students mixed of Boys, Girls