Math Is Fun Forum

You are right, but sometimes, it is important to remember things. We all know that the square root of 2 can be calculated when required, but remembering 1.4142 helps when we are required to solve problems quickly. The mnemonic 'All Silver Ta Cups' was for the benefit of students who may need to know whether Cosθ or Sinθ or Tanθ  is positve or negative for a certain value of θ while solving problems, when time is crucial. 

Robert Recorde, who gave the world the '=' symbol, would be fuming!
What more do I do?
Multiply both sides by n (n ≠ 0,1), we get n=n !
n IS EQUAL TO n. How do I prove that?
Taking Log on both sides wouldn't help, because we would than get 0=0, which gives us absurd results.
When both the sides are raised to the power n, we still get 1=1 !
When both sides are divided by n, we bget 1/n = 1/n which is the same as n=n !
How about some practical methods? Draw a straight line of 1 m. Draw another of 1 m. Both of them would be exactly equal. Or, 1 hour is the same everywhere on the planet!
I give up

Got it, Mathsy! By cutting 4 rectangles from the four corners, a cuboidal box cannot be made as the heights of the two adjacent sides would differ!

There are n vertices (or points) in a polygon of n sides.
The n points can be connected to any other point in nC2 ways.
That is we get nC2 straight lines. But, of these n straight lines form the sides of the polygon.
Therefore, the number of diagonals is equal to
nC2 - n
= n!/(n-2)!(2!) - n
= n(n-1)/2 - n
= [n(n-1)-2n]/2
= [n² -n-2n]/2 = (n²-3n)/2 = n(n-3)/2

The sum of intenral angles of a polygon of n sides is 180(n-2) degrees as rightly replied by Mathsy!

The equation of an ellipse is given by
x²/a² + y²/b² = 1
The height and the width of the rectangle would be 2b and 2a.
Now, from this information, get the value of ba and a.
Substitute in the equation for the ellipse.
You get the equation of the ellipse.
Thereafter, give values for x like -2, -1, 0, 1, 2 etc. and find the corresponding values of y.

Absolutely right, Mathsy!
What happens if we're allowed to cut rectangles?
We get two variables, x and y.
Volume = (30-2x)(14-2y)(2x)
How do we proceed? Any clues?

Square root of a number A is a number B which multiplied by itself gives the number A.
eg
square root of 25 = ±5 (that is +5 or -5, because both +5 x +5 = 25 and -5 x -5 = 25)
square root of 2401 = ±49
square root of 65536 = ±256
square root of 0 = 0
square root of 1 = ±1
square root of 2 = 1.4142135623..........................
square root of 10 = 3.1622776601........................
Those decimals appear because 2, 10 etc are NOT perfect squares.

wcy, i viewed the base converter. It works well.
I tried converting 759 to base 20 and got the right answer

If you all are interested in logical puzzles, here's one:-

A Captain has three smart soldiers under him. The three soldiers are informed that their intelligence is being tested and that the captain has three blue and two red caps. They are made to stand in ascending order of their heights. They are blindfolded and the captain puts a cap, chosen at random, on the heads of the three soldiers. The blindfold is then removed. The captain asks the third soldier whats the color of the cap on his head. The third soldier sees the color of the cap on the heads of the first two soldiers, but he says he is unable to tell the color of the cap on his head.
The Captain asks the same question to the second solider. The second solider takes into consideration the third soldier's reply and the color of the cap on the first soldier, which he is able to see. But, he too is unable to tell the color of the cap on his head.
The Captain then asks the same question to the first soldier. The first soldier has only the replies of the third and second soldiers to draw any conclusion. But he tells the color of the cap on his head. He gives the right answer.

What's the color of the cap on the first soldier's head and how did he answer correctly?

Normally, in such paradoxes, this is where the mistake lies.
Since a² = b²,
it cannot be inferred that a=b.
Taking square root on both sides of an equation should always have the
'±' sign, after the square root is worked out.

That is, it is to be proved that
(abcd..........)^n = a^n+b^n+c^n+d^n..................
Here, both a,b,c,d...etc and n go on and on.
It is easy to say there would always exist a n digit number whose sum of digits raised to the power n is equal to the number. To prove that may be quite difficult. As n becomes higher, the combinations available increase, thereby increasing the possibility of such a number existing.

Good, you liked the website, Tara Witney!
You are wlecome to join the forum!