Science & Mathematics Fun Mathematics Thread

[dogs105]

Starting off with a fun one, as a lot of people "know" that exponential growth is fast, they underestimate how quickly it actually increase.


Imagine you were drawing a graph of a simple exponential, y=2^x. You have a maths book with 1cm squares in a grid. Starting at the bottom left corner you start plotting the points (0,0), (1,2), (2,4), (3,8) etc. and get the familiar exponential curve that you only ever draw the start of.

After just 5cm on the x axis, your graph has gone off the top of the page.

As you move across about 14 cm (5ish inches), you page would need to be bigger than the height of the London Eye to fit your graph.

By the time you get to the width of your A4 page, your graph is stretching 21km in the air - over 2 and a half times the height of Mount Everest.

If you have an x coordinate of 36 cm - just longer than a regular ruler, your y coordinate is greater than the distance from the earth to the moon.

 

[cats_09]

I wish I knew this when I was at school

 

[dogs105]

I wish I knew this when I was at school

View attachment 1844626

I think it's poor for this to not be explained at school. It's just having a proper understanding of multiplication and the fact that it's commutative. I.e. 5 times 4 is the same as 4 times 5. I teach maths teachers, and we try to emphasise understanding rather than only memorising procedures.

 

[Quivorir]

I wish I knew this when I was at school

View attachment 1844626

Somebody posted this in another thread a few weeks ago and it blue my mind. I consider maths one of my strong points and couldn't believe I didn't know this.

 

[cats_09]

I think it's poor for this to not be explained at school. It's just having a proper understanding of multiplication and the fact that it's commutative. I.e. 5 times 4 is the same as 4 times 5. I teach maths teachers, and we try to emphasise understanding rather than only memorising procedures.

The funny thing is that I love maths and even did a maths subject at uni as an elective for fun, but I don't remember having teachers explain things such as the above - though it seems so obvious and something that I should have been able to work out

I used the full graphic calculator, even though a few games got a bit more use than the actual maths features. It was only at uni that my lecturer really supported the using of the graphics calculator to its full potential - at high school it was all about doing everything the long way, showing all workings etc, so the question is, "what's 8% of 25", I'm not sure too many of my teachers would have appreciated me showing that I know it's the same as "25% of 8"

Obviously it's important to have an understanding of what you're doing, why your doing it etc, but like with English class it felt like a lot of the teaching was more about the leanings within the school walls without necessarily having a real world implication. I'm hoping that things have changed since my days at school and there's a better balance

 

[Billy ray]

If you multiply 6 by an even number, the answer will end with the same digit.
The number in the ten's place will be half of the number in the one's place.

Example: 6 x 4 = 24. 6 x 8 = 48

 

[dogs105]

If you multiply 6 by an even number, the answer will end with the same digit.
The number in the ten's place will be half of the number in the one's place.

Example: 6 x 4 = 24. 6 x 8 = 48

6×10 = 60

But secretly 50 and 10 with 5 half of 10

 

[rank and file]

In year 5 the teacher told us the angles of a triangle add up to 180 degrees.
I thought that sounded like bullshit so I spent the next week drawing random triangles and measuring the angles until I conceded defeat.

My favourite triangle

 

[dogs105]

In year 5 the teacher told us the angles of a triangle add up to 180 degrees.
I thought that sounded like bullshit so I spent the next week drawing random triangles and measuring the angles until I conceded defeat.

My favourite triangle

Cool demo: draw any triangle and cut it out. Tear off the corners and line them up - they form a straight line.

 

[rank and file]

Cool demo: draw any triangle and cut it out. Tear off the corners and line them up - they form a straight line.

Here we go.
brb just grabbing some paper and scissors.

 

[dogs105]

In year 5 the teacher told us the angles of a triangle add up to 180 degrees.
I thought that sounded like bullshit so I spent the next week drawing random triangles and measuring the angles until I conceded defeat.

My favourite triangle

A 3D analogue is the Sierpinski Pyramid, where you start with a triangular based pyramid:


The resultant shape is completely connected, but has zero volume and zero surface area.

 

[rank and file]

A 3D analogue is the Sierpinski Pyramid, where you start with a triangular based pyramid:
View attachment 1852545

The resultant shape is completely connected, but has zero volume and zero surface area.

I could watch fractals in nature all day.

 

[dogs105]

Beginning with a square, one can make a Sierpinksi Carpet:




3D analogue is the Menger Sponge:





Menger sponge has zero volume, and infinite surface area.

 

[rank and file]

Beginning with a square, one can make a Sierpinksi Carpet:

View attachment 1852600


3D analogue is the Menger Sponge:

View attachment 1852601



Menger sponge has zero volume, and infinite surface area.

3d squares are doing my head in.

Give me shells.

 

[Caesar]

If you multiply 6 by an even number, the answer will end with the same digit.
The number in the ten's place will be half of the number in the one's place.

Example: 6 x 4 = 24. 6 x 8 = 48

Another handy trick is that transposition mistakes are divisible by 9 - e.g. mistyping 93 as 39 gives you a difference of 54 which is 6 x 9

works with (I think) any pair of numbers with two transposed digits - e.g. 1582 and 1852

was a lifesaver when I got my first job and half of it was punching long lists of numbers into spreadsheets, adding them up, getting the wrong total and then having to find my mistake