An Interesting Number
SECONDARY O-LEVEL MATHEMATICS
By BENIEL SEKA
The number 01022010 is
an interesting number. Can you say why? Look at the number from the left hand
side towards the right and from the right hand side towards the left... You may
notice that it is symmetrical about a line. It behaves almost like the numbers,
which form the Pascal Triangle. Here are some of the numbers in case you have
forgotten them: 1; 11; 121; 1331; 14641. You probably notice that after writing
0102 you repeat the digits in the reverse order.
The 2010 Mathematical
Association of Tanzania Chairperson, Mrs. Ruth Buluda when conducting a
National Committee meeting of the association on 1st February 2010, brought the
number to my attention. “Look at this number,” she had pointed the number 0102201.
“It is very interesting.”
I looked at the
number. “Yes,” I responded, “It is interesting.” I noticed that the number had
represented the date of the meeting, which written as 01.02.2010 indicating the
first day of February for the year 2010. I appreciated the fast way she had
noticed this number. The National Committee meeting is held on every first Monday
of a month except when the day falls on a public holiday. Therefore, this was a
mere coincidence.
This is a very rare
case for dates. I challenge you to identify other dates, which display a
similar behaviour. May be you thought of 11.02.2011. Fine, I like that... Do you think you or your colleague
conducted a mathematics activity? Another one is 12.02.2021. If you will be
alive on the said date, remember to mark it because it is an interesting number.
Don’t forget to conduct a mathematical activity to mark the day. Another
interesting date was the 12th December 2012 at noon written is
figures as
12.12.12.;12:12. It is an interesting pattern, isn’t it?
Symmetry is an
interesting concept and you may wish to know more about it. Place your two hands
on a horizontal table. Imagine a vertical line passing between your two thumbs.
The line becomes the line of symmetry. If a plane mirror were placed on that
line and tilted a bit towards your left hand, it would make a reflection
matching the reflection of your right hand.
You may now be
reflecting on why symmetry is given so much prominence in mathematics. The
perfect balance you see and sense in the shape of a human body, in the body of
a butterfly, in the shape of a leaf, in the perfection of a circle, and in the structure
of a honeycomb cell are all attributed to their symmetry.
The concept of
symmetry appears in nature, art, the sciences, poetry, and architecture.
Actually, symmetry can
be found in nearly every facet in our lives. It is something, which appears so
often, that we just take it for granted. Sometimes a system’s symmetry or lack
of it may be the quality, which makes it appealing. Regardless, when you see
some design or a sculpture, you (almost immediately) like it or dislike it and
its symmetry or lack of it probably influenced your feelings.
Another interesting
number is 12345679. Notice that 8 is not among the digits of this number. What
is interesting about this number is that if you multiply it by 9 you obtain 111
111 111. The string of ones in the product should be interesting too. Common
sense will tell you that if you multiply this product by any of the first nine
counting numbers will give you a similar string of the multiplicand. For
example, 111
111 111x 3=333 333 333.
This result can be
useful in computing interesting products such as 12345679x27; 12345679x3; 12345679x54and soon.
Try them and enjoy the results. You may use a calculator if you have a problem
in multiplying numbers. Can you now
generate more products which make use of this facility and hence create
interesting results?
Mathematically, an
object is considered to possess line of symmetry or point symmetry if you can
find a line, which divides it into two identical parts so that if it were
possible to fold it along that line both parts, would match perfectly over each
other. Recall the case of your two hands where you can match the fingers and
the thumbs together. The following are examples of shapes that hove symmetry:
Example 1:
A circle has infinite
number of lines of symmetry. You can draw several lines through the centre. It
has also point symmetry. All the lines cross at the centre. See figure1. 
Example 2
A rectangle has two
lines of symmetry. The lines meet at the intersection of its diagonals. Note
that for a rectangle, the diagonals are not lines of symmetry. See Figure 2.
Can you find the case of a square? What about a rhombus? Does any parallelogram
possess a line of symmetry?
Example 3
Any isosceles triangle
has only one line of symmetry. See Figure 3. What about an equilateral triangle?
Can you show that it has three lines of symmetry?
In mathematics,
symmetry goes beyond arithmetic and geometry. Using algebra, a function’s
inverse ( symmetrical image) can be found by interchanging its y and x coordinates
From these equations, graphs of the function and its inverse can be drawn and their
line of symmetry will be y=x.. The term, symmetry,
is also applied to relations. For example, the relation “=” possess symmetry
because a=b and b=a both hold true, the relation “a ≥ b” does not have symmetry because in some cases a is greater
than b but there is no case when b is greater than a,
Finally, think of the
movement of a four-legged animal. May be you have observed a a video or a real
situation of a gazelle being chased by a leopard. You may have noticed that
when they are at a great speed their fore legs are parallel to their hind legs.
At this point, the movement of each animal have line symmetry. Do you see that by
studying symmetry you can learn many new things? Keep looking for more symmetry.
END
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