In March of 2003, WTM had the great pleasure and honor to receive some interesting "fan mail", e-mail style of course, from the far-off country of China. It came from a young girl who loves math and had been reading various pages in this site. Let's let her introduce herself now.
My name is Wanting Zhong, and my English name is Helen. I was born on Jan. 24th, 1992 in Chongqing, China, but now I live in Guangzhou, China. Guangzhou is a large city in Southern China and it's also the capital of Guangdong Province. I'm a Sixth-grade student at Nong Lin Xia Lu Primary School here. I have a great passion for mathematics. During Grade 1 and Grade 2, I was solving 'little math goodies' like those presented in 'Number Line Land'. In Grade 3 and Grade 4, I was getting acquainted with algebra, fallacy and geometry. I was solving more difficult problems by then, like those in 'Problem Solving Quizzes'. Now I'm particularly interested in fallacies, paradoxes, infinity, illusions, number trials and famous math discoveries. I'm just algebra-frenzy, fallacy-crazy and illusion-mad! :-) In short, I'm a mathematics maniac!
I'm also a member of the Guangzhou Olympics Math School. I'm in the best class---Class 14. Soon there'll be a national math competition and I'm looking forward to it.
Then, later she said:
I've been on the Internet for quite a long time. I have visited many interesting English math sites, like the Math Forum, Count On, Getsmarter, Mudd Math Fun Facts, etc.. Your site is the most interesting and inspiring. I like the way you never give us the direct answer, but ask us to solve the problems ourselves! That's something special...and cool! Your site is simply fantastic!
It's obvious that this young lady has a very discriminating taste in websites! And we certainly must concur in her opinion.
Before we present some samples of the thinking of this brilliant little math scholar and researcher, we will show you her picture.
Here is our first sample of interesting number trivia that Wanting sent us, on Pi Day in fact (3/14). It's just the kind of number "play" that we like to see here in WTM. She prefaced her discoveries by saying very modestly the following:
I'm very interested in numbers like you. After reading 'Special Numbers (I) (II)' and contemplating for some time, I 'suddenly' thought of something about 91. Maybe it's trivial or naive, even mundane, but it's my first approach to the connections between numbers and I think you may like my ideas. What do you think?
1. Sqrt (91 - SoD (91) ) = 9 * 1
2. 91 ^ 2 = 8281
SoD (8281) = 19 [reverse form of 91]
91 * 19 = 1729
SoD (1729) = 19 [reverse form of 91]
Notice that the first digit and the last digit form a 19.
3. Prime factorization of 91:
91 = 7 * 13
Add the two primes and we get:
7 + 13 = 20 = 19 + 1
Notice that 19 is a prime.
4. 91 - 19 = 72
72 = (9 - 1) * 9
7 + 2 = 9 [first digit of 91]
7 * 2 = 14
SoD (14) = 5
19 - 5 = 14
SoD (91) = 2 * SoD (14)
What do we think? Bravo, Wanting! You're on your way to a marvelous journey through the world of numbers, one that will take up a lifetime, and more.
In the same email, she continued:
Also, I've tried constrained writing as it was introduced in 'Pi Words'. I've 'constructed' a poem using PWs, but it was really odd and it was very uncomfortable writing constrained poetry. My poem is as follows:
Cousin Pen Picky |
almost everything except pastrami
for she's fond of partaking
and never minds if she's fat as a pig
for smoked salmon and meat pie
even on a dangerous turnpike
while her peccavi
says that eating is prime
In a later email (3/25/03), she wrote:
My favorite numbers are pi, 12, 20 and all primes. I think 12 is a very interesting number. I've discovered some curious facts about it.:
If we present the number in this form:
12 = 3 * 4
Then we can see that the equation consists of the first 4 consecutive integers larger than 0, in its correct order, 1, 2, 3, 4. Another example is 56 = 7 * 8. Hmm...
12 is also interesting in some other aspects. Apparently, it consists of the first 2 consecutive integers larger than 0 (this is so obvious). 12 is the multiple of 6, the smallest perfect number. It's the triple of 4, the smallest composite number. It's the quadriple of 3, the first odd prime... Its divisors are:
1, 2, 3, 4, 6, 12
Aren't the first consecutive digits lovely? They correspond with the equation!
If we express it in this way, as the result of two primes added:
12 = 5 + 7
Well, 5 equals 2 plus 3. I once read in a book that 2 is the first 'female' number and 3 is the first 'male' number. 5 is the number of marriage (or something like that). 7 is encountered everywhere: the seven days in a week, the 7 notes in music... And think about 12! the combination!
The prime factorization of 12 yields something too. If we write it out with exponents...
12 = 2^2 * 3
The first three numbers appear! And there are three 2's!
Something better is to come. 12 is an admirable number! Look at this:
1 + 3 + 4 + 6 - 2 = 12
Three cheers for 12!
The reason I like 20 is very simple: it's my student No. at school! (Something that pleases me is that 20 is admirable too:
2 + 4 + 5 + 10 - 1 = 20
By the way, I found out that June 28th is very special! Its digit form 6/28 contains not only two perfect numbers, but also a multiple of 3.14! That's remarkable. Also, 6 + 2 = 8. The sum of its digits is 16, the 4th square, while 4 is the smallest composite number! Add the month and the day and you get 34, the double of 17, which is the 6th odd prime and 7th prime! Ta-dah!
In an email sent on April 17, 2003, she wrote:
Recently, I discovered an interesting phenomenon concerning the 'unlucky' 13:
13^2 = 169 (Note that it can be separated into 16 and 9, two important squares which are used in the Pythagorean Theorem)
Reverse the square and you get 961, which is also a square. But--
sqrt 961 = 31
And 31 is 13 reversed!
SoD 13 = 4
SoD 169 = 16
4^2 = 16
A trivial fact about pi..
Let a = 1, b = 2, c = 3, ... y = 25, z = 26.
Thus p = 16 and i = 9. Both squares! (Which might indicate that pi is very 'square'. Strange thing, huh?)
16 (P) and 9 (I) are famous for their use in the Pythagorean Theorem. And...
1 + 6 + 9 = 16
SoD (16 * 9) = 9
16 and 9 reproduced...Ta-dah!
P.S.: Note that 16 is 4^2 and 9 is 3^2. The first digit and the last digit of 3.14 are 3 and 4.
To be continued...
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