Science & Mathematics The Maths Thread

[Wallaby]

1/7 = .142857142857142857142857.................... The same six digits repeating.

2/7 = .285714285714285714......................... The same six digits repeating and in the same order as 1/7, just starting from a different place.

3/7 = .428571428571..........ditto.
4/7 = .571428.........
5/7 = .714285........
6/7= .857142.................. the same six digits repeating and in the same order as 1/7, just starting from a different place.

The inverse of all prime numbers all show similar patterns (except for 2 and 5).
The number of repeating digits is one less than the number being inverted - example 1/7 is 6 recurring digits, 1/17 is 16 recurring digits etc
EXCEPT
sometimes there are two more patterns of recurring digits in the inverses. For example:
1/13 = .076923 - six recurring digits.
2/13 = .153846 recurring - a different set of 6 recurring digits.

1/13, 3/13, 4/13, 9/13, 10/13 and 12/13 all use the .076923 recurring pattern - the other fractions use the other pattern.

so - Inverse of 13 uses 2 different patterns of 6 digits - 2x6 = 12 (one less than the number being inverted).
Inverse of 3 uses 2 different patterns of 1 digit - 2x1 = 2.
Inverse of 11 uses 5 different patterns of 2 digits - 5x2 = 10.
Inverse of 37 uses 12 different patterns of 3 digits - 3x12 = 36.
Inverse of 41 uses 8 different patterns of 5 digits - 8x5 = 40.
Inverse of 53 uses 4 different patterns of 13 digits - 4x13 = 52.
Etc.....

It is apparently all explainable and fairly trivial, but it blows my mind.

 

[BORK]

5318008

Stole my planned contribution to the thread.

 

[GoTheSwannies]

A customer purchases an item for $5.85.

He gives you a $10 note and a $1 coin.

The till is broken and you don't have an iPhone.

Do you:

(a) work out in your head that the change owed is $5.15
(b) call the manager
(c) go home on stress leave and seek validation via social media

(D) go onto an Internet forum and troll someone to restore a sense of superiority after failing at real life

 

[ChampRevesby]

 

[Gralin]

Hey dogs105

 

[dogs105]

Does anyone have an Erdos number?

4

 

[Shell]

FWIW I was in Yr7 maths this morning, I told the maths teacher about the inverse of percentages are the same.

Her mind was blown.

 

[slider95]

In the AFL today, teams ranked 7th, 8th and 9th on the ladder (irrespectively) play the teams ranked 16th, 17th and 18th.

What is the probability of that occurring at any one time?

 

[Frank Bunn]

In the AFL today, teams ranked 7th, 8th and 9th on the ladder (irrespectively) play the teams ranked 16th, 17th and 18th.

What is the probability of that occurring at any one time?

Chat:GPT says 1/1365.

Spoiler

 

[Norwegian Blue]

4

Same.

 

[kickazz]

Twelve plus One = Eleven plus Two.
#Anagram.

56 squared = 3136.

Each square number goes up by each odd number.

One of those mathematical concepts best proven visually, too: