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冥冥中的数字,数字中的冥冥
送交者: 历程历程 2022年06月05日13:05:59 于 [教育学术] 发送悄悄话

(原创)

Fathomless Numbers 

Today is June 4, 2022, which is the anniversary of the notorious human tragedy, Tiananmen Square Massacre, which happened exactly 33 years ago on June 4, 1989, in Beijing, and was witnessed by people in every corner of the world. 

Each year, the anniversary lapses peacefully without much of an event. However, this year it might unfold itself differently because certain unexplainable mathematical facts come up which may foretell that this year would be special. 

A mathematical approach to the complexity of a large number: As a child, I was told that a large number could be “simplified” to reveal some of its concealed information by carrying out a “cross sum” procedure. 

For example, the cross sum of the number 195853 is 1+9+5+8+5+3 = 31 

The number 31 could then mean something to a person who would like to inquire what information is contained in the number 195853. 

Now we are ready to explore some mysteries associated with this anniversary. 

  1. Anniversary Mystery

    1989 is the year when the massacre happened.

    Cross sum of 1989 = 1+9+8+9 = 27

    2022 is the current year.

    Cross sum of 2022 = 2+0+2+2=6

    27+6 = 33

    Ah, we are in the 33rd anniversary. So, yes, the number 33 unambiguously pops up to signify this year.

    2. Symmetry Mystery

    Since 33 is such a special number, we would like to consider it from all its possible facets or “disguises” including

    33=30+3;

    33 under cross sum = 3+3 = 6;

    33 viewed as 3 times 3 = 9;

    33 viewed as 3 to the power 3 = 3^3 = 3 times 3 times 3 =27.

    With these reinterpretations, we should also consider all fine numerical details of the massacre which often exhibits itself as 641989 or 198964. This has the cross sum 6+4+1+9+8+9=37

    Multiplying 37 by the various reinterpretations of the anniversary number 33, we find

    37 times 33 = 1221 (nice)

    37 times 6 = 222 (nice)

    37 times 9 = 333 (nice)

    37 times 27 = 999 (nice)

    Incidentally, the number 1221 also comes from Cross sum of 641989 times (cross sum of 1989 plus cross sum of 2022) = 37 times (27+6) =1221

    Wow, I was breathless when I came across these “perfect numbers”.

    Are you equally stunned or at least intrigued?

    If not yet, continue to the next puzzle.

    3. Symmetry-Breaking Mystery

    It may be seen that a tiny alteration of the massacre date will spoil all the symmetries observed above.

    For example, if it were dated June 3, then the cross sum of 631989 is 36.

    Thus 36 times 33 = 1188

    36 times 6 = 216

    36 times 9 = 324

    36 times 27 = 972

    Likewise, if it were dated June 5, then the cross sum of 651989 is 38.

    Thus 38 times 33 = 1254

    38 times 6 = 228

    38 times 9 = 342

    38 times 27 = 1026

    Consequently, all the symmetries are lost.

    Whether or not you feel mystified by these facts regarding numbers, the truth is that mathematics does step out to commemorate this special day in its own undeniable and immortal way to present its homage to those who gave up their lives for their faiths and ideals.

    Beyond this, it is up to time to tell.



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