A woodcutter went up the hills to cut trees for his living everyday. One day, he went to the hills as usual. On his way, he saw a wounded little bird. The little bird's body was covered with glittering silver feathers. It was very beautiful. The woodcutter said, " I've never seen such a beautiful bird before." So he took the little bird home and cured its wounds. During the rehabilitation process, the little bird sang to the woodcutter sweet and beautiful songs. The woodcutter felt very very happy.
One day, the woodcutter's neighbour came to visit him and saw the silver bird. He said to the woodcutter, " I've seen a little bird with golden feathers. That gold bird was much more beautiful than your silver bird. Besides, it sang much better than yours."
The woodcutter wondered, "Is there really such a gold bird? How beautiful is this gold bird? Can it sing very beautiful songs?" From then on, the woodcutter began not to enjoy songs sang by the silver bird. Gradually, the woodcutter became more and more unhappy each day.
Now the silver bird fully recovered from its wounds. It was about time for it to fly away. Before it went, it flew to the woodcutter and sang to him for the last time. After the silver bird finished, the woodcutter sighed, "Your silver feathers are very beautiful, but I think you are not as beautiful as the gold bird. Your song is very beautiful too, but still I don't think it's as beautiful as the gold bird sings."
The silver bird then flew to the direction of the setting sun. Under the golden setting sunlight, the bird became a beautiful glittering gold bird. The woodcutter then realized that the gold bird he's been dreaming for so long was really just the one beside him all the time!
Happiness does not rest on how much one possesses, but on how less one bothers. Sometimes we don't appreciate what we are having is already a fortune. We just realize (and regret to realize) only when we lose it. So appreciate what we have and don't make unnecessary comparisons.
Wednesday, May 23, 2012
Wednesday, May 16, 2012
I'm Senior
A senior citizen was driving down the M2 motorway. His car phone rang.
Answering, he heard his wife's voice saying hastily, "George, the news just said that there's a car going the wrong way on M2. Be careful!"
"My goodness!" cried George, "It's not just one car. There're hundreds of them!"
Answering, he heard his wife's voice saying hastily, "George, the news just said that there's a car going the wrong way on M2. Be careful!"
"My goodness!" cried George, "It's not just one car. There're hundreds of them!"
Wednesday, May 9, 2012
We Can Hear Just Fine
Three retirees were playing golf one fine day.
One man remarked to the other, "Windy, isn't it?"
The second man replied, "No, it's Thursday."
And the third man chimed in, "So am I. Let's have a beer."
One man remarked to the other, "Windy, isn't it?"
The second man replied, "No, it's Thursday."
And the third man chimed in, "So am I. Let's have a beer."
Tuesday, May 1, 2012
The Pythagoras Theorem
My point of departure is the Pythagoras Theorem:
Everybody with secondary education knows the Pythagoras Theorem. But I bet over 90% of people don't know why it is true (i.e. they don't know how to prove it)! While proving the Pythagoras Theorem appears to be difficult, I present below a classical proof by Euclid (circa 330 - 260 BC) which requires no more than elementary Geometry known to every secondary student!
Please feel free to skip the rest if Geometric Proof doesn't appeal to you.
First, draw squares ABFG, BCDE and CAHK. Obviously, our task is to prove the area of square ABFG is the sum of the area of square BCDE plus the area of square CAHK. Usually people are stuck at this point. But what Euclid did was to draw a few lines as follows:
. draw CM parallel to AG, cutting AB at N and FG at M respectively
. join BH and CG
With Euclid's hints, the picture now becomes much clearer as in above figure, we can then proceed as follows:
In ΔABH and ΔAGC,
....................... AB = AG ......................... (sides of square ABFG)
.................. ∠BAH = ∠BAC + ∠CAH = ∠BAC + 90°
.................. ∠GAC = ∠GAB + ∠BAC = 90° + ∠BAC
............... ∴ ∠BAH = ∠GAC
...................... AH = AC .......................... (sides of square CAHK)
............... ∴ ΔABH Ξ ΔAGC ...................... (SAS)
....... Area of ΔABH = ½*AH*HK
........................... = ½* (AH*HK)
........................... = ½*(area of square CAHK)
....... Area of ΔAGC = ½*AG*GM
........................... = ½*(AG*GM)
........................... = ½*(area of rectangle AGMN)
Since ΔABH Ξ ΔAGC as proved above,
................ then area of ΔABH = area of ΔAGC
So, ½*(area of square CAHK) = ½*(area of rectangle AGMN)
......... ∴ area of square CAHK = area of rectangle AGMN ......... (1)
Similarly,
............. area of square BCDE = area of rectangle BFMN ......... (2)
Combining (1) and (2) together,
area of square CAHK + area of square BCDE = area of rect AGMN
................................................................... + area of rect BFMN
............................................................... = area of square ABFG
i.e. .............................................. a² + b² = c² .............. Q. E. D.
Everybody with secondary education knows the Pythagoras Theorem. But I bet over 90% of people don't know why it is true (i.e. they don't know how to prove it)! While proving the Pythagoras Theorem appears to be difficult, I present below a classical proof by Euclid (circa 330 - 260 BC) which requires no more than elementary Geometry known to every secondary student!Please feel free to skip the rest if Geometric Proof doesn't appeal to you.
First, draw squares ABFG, BCDE and CAHK. Obviously, our task is to prove the area of square ABFG is the sum of the area of square BCDE plus the area of square CAHK. Usually people are stuck at this point. But what Euclid did was to draw a few lines as follows:. draw CM parallel to AG, cutting AB at N and FG at M respectively
. join BH and CG
With Euclid's hints, the picture now becomes much clearer as in above figure, we can then proceed as follows:
In ΔABH and ΔAGC,
....................... AB = AG ......................... (sides of square ABFG)
.................. ∠BAH = ∠BAC + ∠CAH = ∠BAC + 90°
.................. ∠GAC = ∠GAB + ∠BAC = 90° + ∠BAC
............... ∴ ∠BAH = ∠GAC
...................... AH = AC .......................... (sides of square CAHK)
............... ∴ ΔABH Ξ ΔAGC ...................... (SAS)
....... Area of ΔABH = ½*AH*HK
........................... = ½* (AH*HK)
........................... = ½*(area of square CAHK)
....... Area of ΔAGC = ½*AG*GM
........................... = ½*(AG*GM)
........................... = ½*(area of rectangle AGMN)
Since ΔABH Ξ ΔAGC as proved above,
................ then area of ΔABH = area of ΔAGC
So, ½*(area of square CAHK) = ½*(area of rectangle AGMN)
......... ∴ area of square CAHK = area of rectangle AGMN ......... (1)
Similarly,
............. area of square BCDE = area of rectangle BFMN ......... (2)
Combining (1) and (2) together,
area of square CAHK + area of square BCDE = area of rect AGMN
................................................................... + area of rect BFMN
............................................................... = area of square ABFG
i.e. .............................................. a² + b² = c² .............. Q. E. D.
Monday, April 23, 2012
A380 Experience
Recently I went to Hong Kong with my son to see my grandson, Christian. We flew Qantas QF127 from Sydney to Hong Kong on 8Apr (Sunday). Qantas began flying Airbus A380 between Sydney and Hong Kong on Thursday/Friday/Saturday/Sunday and Boeing 747 on other days from January, 2012. We took the opportunity to try the A380 with that trip.
The A380 is a double-deck aircraft. The first class and economy class are on main deck, and business and premium economy class are on upper deck. Total capacity is 450 passengers with 14 first class, 72 business class, 32 premium economy class and 332 economy passenger seats. Boarding was a bit lengthy given the large passenger loads. Luckily we had boarding priorities as being Qantas frequent flyers. Inflight facilities were new and clean. Inflight entertainments were satisfactory with sufficient varieties. Cabin was generally spacious. Seat space was simillar to other aircrafts. Like boarding, baggage collection took longer than usual with the passenger loads. Overall, the journey was comfortable and enjoyable.
The A380 is a double-deck aircraft. The first class and economy class are on main deck, and business and premium economy class are on upper deck. Total capacity is 450 passengers with 14 first class, 72 business class, 32 premium economy class and 332 economy passenger seats. Boarding was a bit lengthy given the large passenger loads. Luckily we had boarding priorities as being Qantas frequent flyers. Inflight facilities were new and clean. Inflight entertainments were satisfactory with sufficient varieties. Cabin was generally spacious. Seat space was simillar to other aircrafts. Like boarding, baggage collection took longer than usual with the passenger loads. Overall, the journey was comfortable and enjoyable.
Wednesday, April 4, 2012
Blood Types
A. Classification
Everybody's blood looks the same. But under a microscope, distinct differences are visible. Two types of chemical molecules (A and B) can be observed in blood cells. Depending on what chemical molecules are present, bloods can be classified into 4 main types:
A - if the blood cells have only A molecules
B - if the blood cells have only B molecules
AB - if the blood cells have a mixture of both A and B molecules
O - if the blood cells have neither the molecules
In addition, a particular protein may also be present in the blood cells. If the blood contains that protein, it is said to be positive. if not, it is negative. Thus, the blood type can be further classified into 8 types: A+, A-, B+, B-, AB+, AB-, O+, O- accordingly.
B. Matching
If two different blood types are mixed together, the blood cells may begin to clump together in the blood vessel, causing a potential fatal condition. Therefore, it is important that blood types be matched before blood transfusions take place. As shown in Figure 1, type O blood can be given, apart from O itself, to all blood types, A, B and AB. Type A blood can be given, apart from A itself, to blood type AB. Type B blood can be given, apart from B itself, to blood type AB. But type AB blood can be given to AB itself only.
Furthermore, positive blood types can only be given to positive blood types, whereas negative blood types can be given to both positive and negative blood types. As such, the possibilities of blood types for blood transfusion are summarized as in Figure 2 accordingly. As can be seen, blood type O- can be given to all blood types, and hence is usually regarded as 'universal donor'. Blood type AB+ can take any blood types for transfusion, and hence is usually regarded as 'universal receiver'.
C. Popularity
Type O blood is the most common type found in the population (49%), followed by type A (38%) and type B (10%), with type AB being the rarest (3%). Within each of the 4 man blood types, negative blood types are much rarer than their positive counterparts. Figure 3 shows the percentages of Australians with particular blood types.
D. Inheritance
Blood type is determined by a gene (ABO) in chromosome 9. Since chromosome comes in pair; one from each parent, so the gene also comes in pair, one from each parent accordingly. The gene is called type:
A - if it contains genetic material to produce chemical molecule A in blood cells
B - if it contains genetic material to produce chemical molecule B in blood cells
O - if it contains neither of those to produce any chemical molecule in blood cells.
Since one copy of gene comes from each parent's sperm and egg respectively during conception, the resulting gene pair and thus the resulting blood type of the child can be as follows:
From this table, we can then deduce, although a bit more complicated, blood type of the child as inherited from the blood types of the parents:
In addition, the positive/negative aspect of blood type is determined by a separate gene (RH) in chromosome 1. The gene is called type:
+ - if it contains genetic material to produce a particular protein in blood cells
- - if it doesn't contain genetic material to produce the particular protein in blood cells
Similar to the main blood type above. since one copy of gene comes from each parent's sperm and egg respectively during conception, the resulting gene pair and thus the resulting positive/negative blood type of the child can be as follows:
Again, from the table, we can then deduce, albeit much simpler, the positive/negative blood type of the child as inherited from the positive/negative blood types of the parents:
....end
Everybody's blood looks the same. But under a microscope, distinct differences are visible. Two types of chemical molecules (A and B) can be observed in blood cells. Depending on what chemical molecules are present, bloods can be classified into 4 main types:
A - if the blood cells have only A molecules
B - if the blood cells have only B molecules
AB - if the blood cells have a mixture of both A and B molecules
O - if the blood cells have neither the molecules
In addition, a particular protein may also be present in the blood cells. If the blood contains that protein, it is said to be positive. if not, it is negative. Thus, the blood type can be further classified into 8 types: A+, A-, B+, B-, AB+, AB-, O+, O- accordingly.
B. Matching
If two different blood types are mixed together, the blood cells may begin to clump together in the blood vessel, causing a potential fatal condition. Therefore, it is important that blood types be matched before blood transfusions take place. As shown in Figure 1, type O blood can be given, apart from O itself, to all blood types, A, B and AB. Type A blood can be given, apart from A itself, to blood type AB. Type B blood can be given, apart from B itself, to blood type AB. But type AB blood can be given to AB itself only.
Furthermore, positive blood types can only be given to positive blood types, whereas negative blood types can be given to both positive and negative blood types. As such, the possibilities of blood types for blood transfusion are summarized as in Figure 2 accordingly. As can be seen, blood type O- can be given to all blood types, and hence is usually regarded as 'universal donor'. Blood type AB+ can take any blood types for transfusion, and hence is usually regarded as 'universal receiver'.
C. PopularityType O blood is the most common type found in the population (49%), followed by type A (38%) and type B (10%), with type AB being the rarest (3%). Within each of the 4 man blood types, negative blood types are much rarer than their positive counterparts. Figure 3 shows the percentages of Australians with particular blood types.
D. Inheritance
Blood type is determined by a gene (ABO) in chromosome 9. Since chromosome comes in pair; one from each parent, so the gene also comes in pair, one from each parent accordingly. The gene is called type:
A - if it contains genetic material to produce chemical molecule A in blood cells
B - if it contains genetic material to produce chemical molecule B in blood cells
O - if it contains neither of those to produce any chemical molecule in blood cells.
Since one copy of gene comes from each parent's sperm and egg respectively during conception, the resulting gene pair and thus the resulting blood type of the child can be as follows:
| Gene Type from One Parent | Gene Type from Another Parent | Gene Pair of Child | Blood Type of Child |
| A | A | AA | A |
| A | B | AB | AB |
| A | O | AO | A |
| B | B | BB | B |
| B | O | BO | B |
| O | O | OO | O |
From this table, we can then deduce, although a bit more complicated, blood type of the child as inherited from the blood types of the parents:
| Blood Type of One Parent | Gene Pair of One Parent | Blood Type of Another Parent | Gene Pair of Another Parent | Gene Pair of Child | Blood Type of Child |
| A | AA or AO | A | AA or AO | AA, AO or OO | A or O |
| A | AA or AO | B | BB or BO | AB, AO, BO or OO | A, B, AB or O |
| A | AA or AO | AB | AB | AA, AB, AO or BO | A, B or AB |
| A | AA or AO | O | OO | AO or OO | A or O |
| B | BB or BO | B | BB or BO | BB, BO or OO | B or O |
| B | BB or BO | AB | AB | AB, BB, AO or BO | A, B or AB |
| B | BB or BO | O | OO | BO or OO | B or O |
| AB | AB | AB | AB | AA, AB or BB | A, B or AB |
| AB | AB | O | OO | AO or BO | A or B |
| O | OO | O | OO | OO | O |
In addition, the positive/negative aspect of blood type is determined by a separate gene (RH) in chromosome 1. The gene is called type:
+ - if it contains genetic material to produce a particular protein in blood cells
- - if it doesn't contain genetic material to produce the particular protein in blood cells
Similar to the main blood type above. since one copy of gene comes from each parent's sperm and egg respectively during conception, the resulting gene pair and thus the resulting positive/negative blood type of the child can be as follows:
| Gene Type from One Parent | Gene Type from Another Parent | Gene Pair of Child | +/- Blood Type of Child |
| + | + | ++ | + |
| + | - | +- | + |
| - | - | -- | - |
Again, from the table, we can then deduce, albeit much simpler, the positive/negative blood type of the child as inherited from the positive/negative blood types of the parents:
| +/- Blood Type of One Parent | Gene Pair of One Parent | +/- Blood Type of Another Parent | Gene Pair of Another Parent | Gene Pair of Child | +/- Blood Type of Child |
| + | ++ or +- | + | ++ or +- | ++, +- or -- | + or - |
| + | ++ or +- | - | -- | +- or -- | + or - |
| - | -- | - | -- | -- | - |
....end
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