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#43551 This is Cool » I discovered...... » 2005-09-11 19:59:49
- Jai Ganesh
- Replies: 1
I discovered this morning there is a cool website on the net that gives you a lot of information on interesting properties of numbers. There's a lot you can learn, like......
Omega constant is 0.567143290409783872999968662210355549753815787.........
which satisfies each of these simple equations (all equivalent):
e^x = 1/x x = ln(1/x) = - ln(x)
e^-x = x -x = ln(x)
x*e^x = 1 ln(x) = 0
x^1/x = 1/e x/ln(x) = -1
x^-1/x = (1/x)^(1/x) = e ^( ln(x)/-x) = 1
#43552 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-09-11 00:16:57
Problem # k + 22
Grandpa: "My grandson is about as many days as my son is weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 160 years. Can you tell me my age in years?"
#43553 Jokes » Mathematicians are Funny! » 2005-09-09 19:33:24
- Jai Ganesh
- Replies: 0
Fermat's Last Theorem
Like most mathematicians, Pierre de Fermat studied many problems for his own amusement. Indeed, many of his most important contributions were initially scribbled in the margins of books or in notes to friends.
One day in 1637, he made a curious note in his copy of Diophantus's Arithmetic: "The equation x^n + y^n = z^n, where x, y, and z are positive integers, has no solution if n is greater than 2... I have discovered a most remarkable proof, but this margin is too narrow to contain it."
Georg Cantor
Between bouts of insanity and frequent hospitalizations, Georg Cantor laid the foundations of set theory and the study of infinity. In 1878, the young mathematician discovered that there are in fact as many points on the minutest line segment as exist in all of space. Cantor, too, was incredulous. "I see it," he wrote to a colleague, "but I don't believe it!"
Peter Dirichlet
Such was his admiration of Karl Friedrich Gauss that the German mathematician Peter Dirichlet is said to have slept with Gauss's Disquisitiones Arithmeticae under his pillow.
Srinivasa Ramanujan: 1729
Srinivasa Ramanujan was a mathematical prodigy. "I remember once going to see him when he was lying ill at Putney," the mathematician G. H. Hardy once remarked. "I had ridden in taxicab number 1729, and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen.
"'No,' he replied, 'it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.'"
Paul Erdos : 2½ Billion year old
Paul Erdos :"In 1970, I preached in Los Angeles on `my first two and a half billion years in mathematics.' When I was a child, the Earth was said to be two billion years old. Now scientists say it's four and a half billion. So that makes me two and a half billion. The students at the lecture drew a timeline that showed me riding a dinosaur. I was asked, `How were the dinosaurs?' Later, the right answer occurred to me: `You know, I don't remember, because an old man only remembers the very early years, and the dinosaurs were born yesterday, only a hundred million years ago.'"
#43554 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-09-09 18:03:26
Problem # k + 21
If the diagonal and the area of a rectangle are 25 m and 168 m², what is the length of the rectangle?
#43555 Re: Maths Is Fun - Suggestions and Comments » hide buttons work when logged in » 2005-09-08 22:58:48
Yes, that would be fine! When the question or problem is no longer current, the hide tag would show the solution! Good thought 
#43556 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-09-08 21:22:32
Problem # k + 20
What is the least number that should be multiplied to 100! to make it perfectly divisible by 3^50?
#43557 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-09-08 16:58:33
Problem # k + 19
At his usual rowing rate, Rahul can travel 12 miles downstream
in a certain river in six hours less than it takes him to travel the same
distance upstream. But if he could double his usual rowing rate for his 24
mile round trip, the downstream 12 miles would then take only one hour
less than the upstream 12 miles. What is the speed of the current in miles
per hour?
#43558 Re: Maths Teaching Resources » hehehe » 2005-09-08 16:19:36
... but in the end...he didn't pass the exam and I felt a little guilty : (
During 1999-2000, I was teaching a student iin her Pre-University four subjects....Mathematics, Physics, Chemistry and English...French and Computer Science she learnt by herself...She passed in all subjects other than Mathematics...initially I felt guilty, because I knew Mathematics was the weakest link...but I didn't give up....I taught her Mathematics for two more years, she finished her Bachelor of Computer Applications and is now doing her MBA in London! I had to learn Digital Logic Fundamentals and Accountancy to teach her for her BCA, now I am delighted!
Sometimes, you teach and the student doesn't perform well.....are the teachers to blame? I'd say No.....
#43559 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-09-06 17:49:17
#43560 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-09-05 21:35:18
Problem # k + 18
Persons x and y have the following conversation:
x: I forgot how old your three kids are.
y: The product of their ages is 36.
x: I still don't know their ages.
y: The sum of their ages is the same as your house number.
x: I still don't know their ages.
y: The oldest one has red hair.
x: Now I know their ages!
How old are they?
#43561 Re: Guestbook » science » 2005-09-05 20:32:18
Lord Ganesh was born on the 4th day of the bright fortnight of the month of 'Magh'. 'Chatur' means 4. He controls the 8 directions of the Cosmos. 'Gana' means to count. (Ganith or Ganitham is Mathematics in Hindi/Sanskrit/Tamil) The science of Astrology is dependant on numbers. Hence Lord Ganesh is the Master of Astrology. No wonder that one worships Lord Ganesh before embarking on anything auspicious.
Lord Ganesh's big ears denote that He can hear and understand Vedantic Truth. His big head reminds us that we are Spiritual Creatures so we must 'Think Big'. His small mouth denotes that He talks less. (So must we: Talk less and Listen more) His small eyes urge us to 'focus'. The long trunk of an elephant has the quality of being able to uproot a tree, and at the same time pick up a tiny needle from a haystack. This is again a quality attributed to the Lord, as we believe that in spite of His great power, the tiniest creature does not pass unnoticed by Him. The mouse though small can play havoc. Ganeshji has him under His control. Lord Ganesh's large belly denotes prosperity and that He digests all the good and bad in the world. The planet Mars and Ganpati are considered to have the same complexion. On Ganesh Chaturthi frequencies from Mars and Ganesh reach the Earth.
Ganeshji holds in His 4 hands:
An axe to cut off evil and worldly attachments.
A Rope pulls His disciples closer to the Spiritual Path.
The Rosary beads remind one to continuosly strive towards the Real Knowledge.
The last hand is held up in a posture of blessing.
May the Lord Ganesh bestow His Grace upon all of you today.
#43562 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-09-05 19:27:38
Problem # k + 17
A rectangular pool 20 meters wide and 60 meters long is surrounded
by a walkway of uniform width. If the total area of the walkway is 516 square meters, how wide, in meters, is the walkway?
#43563 Re: Guestbook » science » 2005-09-05 16:17:12
Oh yes, MathsIsFun!
Lord Ganesh is the first worshipped God by all following the Hinduism faith.
Elephant headed, Lord Ganesh is worshipped for Wisdom, among other things. Chaturthi is the fourth day after the full moon or the new moon.
Ganesh Chaturthi is celebrated all over the world, all over India, but it is the most important festival in Maharashtra/Goa state (Mumbai, known as Bombay earlier, is the capital of Maharashtra state).
All poojas are done after worshipping Lord Ganesh first. You can notice a shrew near Lord Ganesh's feet. That is his avatar. Lord Ganesh is known by many names....Vinayak, Ganapathi, Vignesh, Lambodar etc.
On this day, idols of Lord Ganesh are made of clay and worshipped with flowers, sweets, coconut etc. After three days/ten days, the idols are taken in a procession and dipped in a river/sea. It is a very colorful festival.
My mother worshipped this God and I was born on Ganesh Chaturthi in the year Neil Armstrong, Michael Collins and Edwin Aldrin created history!
No wonder my name is Ganesh!
Lord Ganesh
#43564 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-09-05 16:05:39
John, you went wrong somewhere; please try again
#43565 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-09-04 18:26:46
Solution to Problem # k + 6
You are right, John. I don't know the reason. Just as MathsIsFun thought, I too believed 97531 x 86420 would be the highest product!
Problem # k + 16
The pages in a book are serially numbered from 1. If the number of digits required to total all the pages in the book is 972, how many pages are there in the book?
#43566 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-09-04 16:14:07
Problem # k + 15
A sample of x litres from a container having a 60 litre mixture of milk and water containing milk and water in the ratio of 2 : 3 is replaced with pure milk so that the container will have milk and water in equal proportions. What is the value of x?
#43567 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-09-04 16:00:55
Good work, John E. Franklin
Solution to Problem # k + 14
Any triangle you try to draw with the maximum area would have same base and height. The solution is, without doubt, lw/2. You can try all possibilities. You'd get the same answer, both when the base is 'l' and 'w'.
Solution to Problem # k + 12
Yes, you would be one equation short. But, when you get one number is eight times the other, the numbers would have to be 1 and 8, as each number a,b,c, and d is a single digit number!
Solution to Problem # k + 10
Yes, 5121 is the correct answer. As you said, there may not be another as 0242 is not acceptable!
Solution to Problem # k + 11
You have given a different property! I had this is my mind.
It is a number of the form abcd equal to (a^b)*(c^d)
Solution to Problem # k + 6
You are correct. The ages of the grandmother and the grandson would be (61,1), (62,2), (63,3), (64,4), (65,5), and (66,6).
#43568 Re: Jokes » Mathematics jokes » 2005-09-03 20:10:51
Q: What did the baby acorn say when it grew up:
A: Gee, I'm a tree! (Geometry)
Q: What did the ship captain say when his ship got bombed?
A: Deck a Gone!
Q: What do you call a tall coffee pot while it's making coffee?
A: High pot in use (hypotenuse)
Q: Why do computer scientists confuse Christmas and Halloween?
A: Because Oct 31 = Dec 25
Q: What did the circle say to the tangent line?
A: "Stop touching me!"
Q: What's purple and commutes?
A: An abelian grape.
Q: Why is it that the more accuracy you demand from an interpolation function, the more expensive it becomes to compute?
A: That's the Law of Spline Demand.
#43569 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-09-03 19:02:29
Problem # k + 14
What is the area of the largest triangle that can be fitted into a rectangle of length 'l' units and width 'w' units?
#43570 Re: Introductions » Hi everyone! » 2005-09-03 18:54:36
Good wishes, Lizdarryl!
#43571 Re: Help Me ! » the wierd "w" » 2005-09-03 18:47:20
It is omega, and looks a little like w.
In physics, omega stands for angular velocity.
w = dθ /dt where θ is angular displacement and t is time.
In many electricity/magnetism formulae, 2*pi*w is found.
The unit of angular velocity is radians and 2*pi radians is equal to 360 degrees.
Interestingly, alpha is angular acceleration, dw/dt or d²θ /dt².
The Greek alphabets are used to represent various parameters in Physics, like mu is refractive index, rho is specific gravity (and specific resistance too), lambda is wavelenght etc.
#43572 Re: Jokes » Clean Jokes » 2005-09-03 18:30:27
Why was the Egyptian boy confused?
Because his dad became a mummy
#43573 Re: Jokes » Limericks » 2005-09-03 18:28:08
No, I got them from elsewhere...and I enjoyed reading them, so I wanted to share with you all
Here are two more.......
If inside a circle a line
Hits the center and goes spine to spine
And the line's length is "d"
the circumference will be
d times 3.14159
If (1+x) (real close to 1)
Is raised to the power of 1
Over x, you will find
Here's the value defined:
2.718281...
#43574 Re: Puzzles and Games » Two trains » 2005-09-02 18:14:43
Total distance to be covered = 360 m
In the same direction, time taken = 60 seconds, speed = 6m/s
(This is t1-t2, where t1 is speed of the faster train and t2 is the speed of the slower train).
In opposite direction, time taken = 10 seconds, speed = 36m/s
(This is t1+t2)
Solving the two equations, t1=21 m/s and t2=15m/s
#43575 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-09-02 17:42:49
You got it right! Well done! Try the earlier unsolved problmes.
The number of ways of choosing the first square is 64. The number of ways of choosing the second square is 63. There are a total of 64 * 63 = 4032 ways of choosing two squares.
If the first square happens to be any of the four corner ones, the second square can be chosen in 2 ways. If the first square happens to be any of the 24 squares on the side of the chess board, the second square can be chosen in 3 ways. If the first square happens to be any of the 36 remaining squares, the second square can be chosen in 4 ways. Hence the desired number of combinations = (4 * 2) + (24 * 3) + (36 * 4) = 224. Therefore, the required probability = 224/4032 = 1/18