The Maths Thread

Marvin. said:
I am revisiting algebra before I look at calculus so that I do not forget. I created this in python matplotlib to show the inverse relationship between e^x and the natural log. I know you know this but I wanted to remember because if you don't use it you lose it.

View attachment 165858
Click to expand...


ln(e^x) = x and e^(ln(x)) = x

not to be confused with log, of course.
 
1757025232635.png
To show that y=cos(x) is a phase shift of +pi/2 from y=sin(x). I have forgotten a lot of basic maths, so I am re-visiting it this Summer, and I think that if I run examples in matplotlib, it will help me to remember.
 
Marvin. said:
View attachment 168639
To show that y=cos(x) is a phase shift of +pi/2 from y=sin(x). I have forgotten a lot of basic maths, so I am re-visiting it this Summer, and I think that if I run examples in matplotlib, it will help me to remember.
Click to expand...
I seem to recall sin(x)=cos(90-x) so if 2pi is 360 then pi/2 is 90 degrees, and your phase shift is correct.
 
Finished my online course. Usually graphs are rectangular i.e. y vs x but in the graph below, I have plotted the variable r against x in polar coordinates to produce a 'cardioid'.

At x = 0 degrees r=1, and at x=90 degrees, r=0, at x=270 degrees, r = -2.

This shapes follows from the sine wave and its symmetry around it peak at pi/2.

1757428036033.png
 
Working on limits now at the beginning of calculus. This graph displays the function y= x.sin(1/x). You can show by the squeeze theorem that the limit as x approaches 0 that the limit is 0 but graphs are easier. It takes me some time to realise why the graph appears the way it does but it does make sense, and it has a very pleasing shape.

This limit and others are explained in the Youtube video playlist I am following

1761395022556.png


 
Are there some fractions that have more equivalent fractions? The fact you can simply double and keep doubling every fraction would seem to indicate every fraction has an infinite number of equivalent fractions I.e 2/3 = 4/6 = 8/12
3/7 = 6/14 = 12/28 etc etc

But what about fractions that you can also divide to get a equivalent fraction:

4/6 = 8/12 = 16/24 etc etc ad infinitum but also 4/6 = 2/3

So does 4/6 have more equivalent fractions than 3/7?
 
You must log in or register to reply here.
Unread Posts

Don't have an account? Register now and see fewer ads!

SIGN UP
Back
Top