Math Is Fun Forum

The sum of the lengths of any two sides is greater than the lenght of the third side.
For all triangles,
by cosine rule,
c²=a²+b²-2abcosC
(a+b)²=a²+2ab+b²
a+b=√(a²+2ab+b²)
c=√(a²+b²-2abcosC)

now, a+b is definitely larger than c, as the maximum possible value of -2abcosC is less than 2ab, as angle C is smaller than 180 but larger than 0.

if the ellipse is not centred at the origin, the equation becomes,

(x-p)²/a² + (y-q)²/b² = 1

where (p,q) is the centre

here is a proof for right angled triangle:
by pythagoras theorem,
a²+b²=c²
c=√(a²+b²) ----(1)

(a+b)²=a²+2ab+b²

a+b=√(a²+2ab+b²) ----(2)

comparing (1) and (2),
one can see that
a+b>c

Another simple way of doing it is to let x=0.9999999

then, 10x=9.9999999999

Equation (2)-(1),
9x=9
x=1

I am not sure if this is mathematically correct

ok thanks

Physicist joke

There was a serious case of a bird flu and three scientists were called to investigate.

The biologist dissected the chicken and checked for any virus in the chicken.

The chemist went to the neighbouring river and checked for any poisonous chemicals in the river.

The physicist just looked at the chicken and said, "Assuming that the chicken is a perfect sphere..."

here are some tips to remember square root of large numbers..

you can break up the square root into two or more parts, eg

√36=√4 x √9 =2x3=6
that way, you need to remember less values
but this can only work for some numbers

i created a base converter before,
maybe it might be useful to convert your integers to other bases (eg base 16)

http://www.geocities.com/chengyuanwu/baseconverter.html

well, it is not meant for real encryption, just for fun!

there is another encryptor that can encode into special Chinese characters:

eg:
琶抢楸楸⫸ὀ暊煈ὀ暊灎ὀ歬汦煈ὀ橲抢庺歬煈ὀ掜汦潔ὀ潔抢庺楸ὀ抢歬悮潔瘪浠煈暊汦歬⫸ὀ构牂灎煈ὀ掜汦潔ὀ掜牂歬›ಲৄಲৄ煈斐抢潔抢ὀ暊灎ὀ庺歬汦煈斐抢潔ὀ抢歬悮潔瘪浠煈汦潔ὀ煈斐庺煈ὀ悮庺歬ὀ抢歬悮汦憨抢ὀ暊歬煈汦ὀ灎浠抢悮暊庺楸ὀ䅮斐暊歬抢灎抢ὀ悮斐庺潔庺悮煈抢潔灎㢤ಲৄಲৄ

again, it is not really secure since one symbol only codes for one letter

i suspect that it is illegal to square root both sides, since square rooting a negative number is not allowed