Math Is Fun Forum

Hello Everyone!

I need to draw a logo representing the earth in the solar system

It looks like this:

1) An perfect circle to represent the earth

2) a 22.5 degree slanted ellipsoid to represent the equater on the earth

3) several longitude lines from north pole to south pole that intersects with equater

Can you model equater and longitude lines by elliptic equations?

Any help is appreciated

Recently I had a hard time to educate coders that float numbers cannot be used in finance because of lack of accuracy.

They are all educated in a prestigious university specializing in computer science.

However the good old fundamentals seem to have gone from the courses they have taken, and from the coding field in general.

What is a float number?

A binary number with a given bits allowed before the binary point and after it.

For example:

110.0
-0.00001

The former will transform to decimal as 8+4=12,
while the latter will transform to decimal as -1/32 or equivalent.

The integer part is fine from and to decimal 12 <-> 110
But the fractional part (less than 1) has a natural inaccuracy
In decimal if you have a finite fraction that could be some integer multiple of power of 1/10
0.4
or 0.44
you will find it is not possible to transform it to finite fraction on 1/2
0.4 = 0.25+0.125+(0.025) = 0.25+0.125 + 0.015625+0.0078125 +(0.0015625)
-> 0.01100110011...

Of course the computer will simply cut off from some digits after the point

Thus you if you type in a float 0.4 into the computer, it looks as if normal 0.4,
but it will show off inaccuracy at the long end if you multiply a simple integer to it, say 3.
Because the programming language knows it will generally be inaccurate and usually round the last digit before presentation.
As you magnify the discrepancy by the multiplication, the programming language tells the little secret off.

The solution?
Almost all programming language and traditional database have a "decimal" number type.
A "decimal" number is actually two - the integer of the the number string, and the number of figures after the decimal point.
3.14 = Dec(314,2)
Thus the decimal is perfect for financial calculations to store, plus, minus or multiply.

A Moment in Statistics is just the expectation of the power of a random variable:

the moment generating function is  the expectation of the exponential of a small number t multiplied by the random variable:

and the nth moment of x is generated by taking derivative at t=0 of this function

there is an alternative to moment - cumulant

the definition is taking the derivative of the log of MGF in the same manner the moment is generated

What is the rational for the definition of cumulants ?