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Fun With Maths-1

2006-05-23T01:37:00.000-07:00

Fun with mathematics

Computing in a different way

Suppose we want to find the answer for 92 x 86, it can be done in a very simple way, though initially it may appear a bit lengthy.

Step I: Subtract 100 from both the numbers separately:

92 – 100 = -8 (i)
89 – 100 = -11 (ii)

Step II: Multiply the difference obtained as above:

-8 x –11 = 88 (iii)

Step III: Subtract the answer of equation (i) from second number or vice versa

89-8 = 81 (iv)
92-11 = 81 (v)

Step IV: The answer for the product 92 x 86 is obtained by putting result of equation (iv) or (v) at thousand’s and hundred’s places and equation (iii) at ten’s and one’s place, i.e. 8100 = 88 = 8188.

Let us take another example, i.e. product of 92 and 88. Going through the same steps as mentioned above, the results will be as given below:

Step I
92 – 100 = -8
87 – 100 = -13

Step II
-8 x –13 = 104

Step III
92 – 13 = 79
87 – 8 = 79

Step IV
In this case the result from step II has hndred’s place as well, this will be added to the result from step III, because the result of step III gives hundred’s place. So the answer will be: 7900 + 104 = 8004.

Let us take another example, where the numbers are grater than 100, ca 114 and 108. The same sequence of steps will be used in this case also.

Step I
114 – 100 = 14
108 – 100 = 8

Step II
14 x 8 = 112

Step III
114 + 8 = 122
108 + 14 = 122
(8 or 14 are added here because the algebraic sign of the numbers is plus)

Step IV
Add hundred’s place from step II to the answer from step III and the answer is: 12200 + 112 = 12312.

Let us take another example where one number is more than 100 and other is less than 100. Suppose the numbers are 119 and 92.

Step I
119 – 100 = 19
92 – 100 = -8

Step II
19 x –8 = -152

Step III
119 – 8 = 111
92 + 19 = 111
(19 is added here because the algebraic sign of 19 is plus and 8 is subtracted because the algebraic sign of 8 is minus)

Step IV
Add hundred’s place from step II to the answer from step III, ignore sign of step II and the answer is: 1110 – 152 = 10948 (subtraction carried out in this case because answer from step II is negative).

More interesting ways of computing will be shown in next article on Fun with Mathematics.

Where did One Dollar Go?

Three men went to a hotel and stayed there for a night. While checking out, the hotel accountant asked them to pay @ US $10 each and a total of US $30 all-inclusive. As soon as the three left the hotel, recollected that there was discount of US $ for a group booking of three persons. He immediately sent of his room boys to return them US $5. The room boy, while on the way, thought that it would be difficult to divide five dollars among three persons. So he kept two dollars with him and equally distributed three dollars among the three, giving one dollar to each of them. Now arises the problem of accounting.
Each of the three persons got one dollar back, so each one of them paid nine dollars. The room boy kept two dollars with him. That makes a total of US $ 29 (9*3 + 2 = 29). But they had actually paid a total of US $30. Where did the remaining One Dollar get lost in the process?

Answer in next article on Fun With Mathematics.

Diet minerals with antagonistic behaviour

2006-05-18T07:46:00.000-07:00

Iron deficiency is known to cause anemia and zinc excess is known to lead to anemia. But both these elements are essential for body growth and sustenance. Therefore, it is required to maintain a balance of these two elements in our body. This article describes role of these elements in our body metabolism.

Iron
The source of energy for our body is the food we take. But simply taking food does not provide us energy. The food undergoes controlled combustion in our body by reacting with oxygen we breath in. The oxygen is transported from the lungs to various muscles and body parts by blood. Hemoglobin, the red pigment in blood, is the chemical responsible for transportation of oxygen. A part of this hemoglobin molecule is known as hemin, which has iron bound to it. It is the formation of reversible oxygen-hemin complex that enables hemoglobin to carry oxygen from lungs to the various parts where it is required. The important factor in hemoglobin as oxygen carrier is the reversibility of the process. Carbon monoxide (CO) and cyanide (CN-) can occupy the site of oxygen strongly or irreversibly and thus prevent transfer of oxygen. That makes these chemicals toxic.
In the whole process of oxygen transfer and hence for energy requirement of body, hemoglobin and iron in hemoglobin are important. We can say iron helps our cells "breathe” and is the key to strong blood. The body stores iron in the liver, spleen, and bone marrow. A more common problem for humans is iron deficiency, which leads to anaemia. Symptoms include feeling weak and tired. A man needs an average daily intake of 7 mg of iron and a woman 11 mg.
Eating excessive amounts of iron-rich foods has been associated with a higher risk of heart disease. Also doses more than 20 mg per day may cause stomach upset, constipation and blackened stools. Getting the right amount of iron in our diet is important. The amount of iron we need depends on age, gender, and activity level. For example, iron needs increase during periods of rapid growth, such as during pregnancy, childhood, and adolescence when new tissue is being built. Women and teenage girls need more iron than men because of menstrual losses. Active sports persons may also need higher iron intake. Most individuals can obtain enough iron from foods and do not require a supplement.
The vegetarian diets rich in Iron is are dark green vegetables, and the browns of whole grains. Fortified cereals and breads also are good sources of iron. The body absorbs iron better when the iron is from plant sources or combined with foods rich in vitamin C. Cooking foods in cast iron pots, which has been traditionally done in India, adds iron to our diet.

Zinc

Zinc is a trace element that is essential for human health. Deficiency of zinc in body can have following effects:
• loss of appetite,
• decreased sense of taste and smell,
• slow wound healing and skin sores and
• birth defects.

It is also believed to possess anti-oxidant properties, resulting in protection against premature aging of the skin and body muscles. This mineral increases the production of white blood cells that fight infection and helps them fight more aggressively. Zinc increases the number of infection-fighting T-cells, especially in elderly people who are often deficient in zinc, and whose immune system often weakens with age. It also increases killer cells that fight against cancer and helps white cells release more antibodies. Zinc supplements have been recommended for cancer patients. Excess of zinc can cause health problems, such as:
• stomach cramps,
• skin irritations, vomiting,
• nausea and
• anaemia.
Recommended daily dose of zinc is 15 mg to 25 mg. Doses more than 25 mg may cause anaemia and copper deficiency. Very high levels of zinc can damage the pancreas and disturb the protein metabolism. Too much zinc in the form of supplements (more than 75 milligrams a day) can inhibit immune function.
Beans are good vegetarian source of zinc. In case of deficiency and to improve immune system, zinc-fortified cereals can help. The spices commonly used in Indian food system, such as Asafoetida, Cardamom, Cloves Dry, Fenugreek Seed, Garlic Dry, Ginger Fresh are also good sources of both these minerals, i.e. iron and zinc.

Water Shortage in Summer – How to Handle It

2006-05-16T04:45:00.000-07:00

It was first week of May. The summer heat was scaling new heights every day. I was standing at a railway station. Everyone was watching a water fountain and cursing railway authorities – “Look, how wealthy is this department. Janta is not getting water and this department can afford to waste water”. Actually there was a leak in a water supply line. Everyone’s grumbling at the platform was of no avail. I walked down to one of the offices at the platform and informed a railway official about the situation. He immediately told some one to close the water line and take up repairs. This reminded me of an age-old saying – “Don’t curse darkness, instead light a candle”.

Summer in India does not come with heat alone. It brings other problems as well, like scarcity of water and shortage of electricity. One can do without electricity, but it is difficult to live without water.

After this incidence, I thought, if not completely, at least to some extent, water shortage problem can be resolved by our efforts. The citizens can contribute by adopting a conservationist approach without jeopardizing their requirements. Each family can make conscious efforts in this direction and make life comfortable for themselves as well as for their friends and neighbours. An awakened resident alone can do a lot for oneself instead of depending solely and meekly on someone else (authorities) to act for them.

The major contribution can definitely come from those who can afford for it. Here are a few ways to save water.
Close water tap(s) when not in use
If any tap / source of water is found leaking, inform the service department for immediate repair
Use a glass tumbler instead of running water while brushing your teeth. This saves at least five litres of water each time per family member.
Use shaving mug (for water) instead of running water. This again saves at least five litres of water each time per family member.
Open the tap as less as possible, only to meet requirements, while washing your hands. This saves at least 3 litres of water each time per family member.
If you use a shower to bathe, then shut it while applying soap. This saves at least 10 litres of water each time per family member.
Old system in water closet (WC) flushes 10 to 13 litres of water in one gush. New systems provide options of using 3 litres or full 10 litres depending on requirement. If each member of a family uses the former option in the new system at least twice daily, then a family of four members saves 56 litres of water per day. One inch pipe half-turn valve is another simple, but effective system in WC.
The above practices, if followed religiously, give an opportunity for saving at least 100 litres of water per family per day.
Other areas of water wastage are - ignorant and careless usage of ware while car- washing and gardening. Here again, lots of water can be saved by adopting the right practices, as suggested below:
A car can be easily washed with 2 - 3 buckets (about 30 - 40 litres) of water. Using running water from a hose will drain about 400 litres of water in just 10 minutes.
Use of a 'water can' for watering plants in the kitchen garden, instead of a running hose again saves a lot of water.
Rain harvesting is another concept, which at present is being adopted in isolation in those areas where there is only seasonal rain. This concept when developed at large scale can do a lot good for everyone.
Civil authorities and responsible builders can play a big role by making water conservation practices mandatory. It is high time we start adopting these measures before the problem takes monstrous shape.