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E17andy
1318503.  Thu Apr 04, 2019 4:43 am Reply with quote

In the episode recorded, last night (Wed 3rd April), Sandi showed the following:

1, 2, 4, 8, 16, 31... The question was "What is wrong with this?"

The answer was nothing, or we don't have enough information.

Sandi then showed circles with an increasing number of dots, the dots being joined by chords, which divided the circle up into segments.

1 dot, produced 1 segment, 2 dots, 2 segments, etc. and apparently 6 dots produces 31 segments.

Having draw this out, I always get 30 segments and not 31!

Am I doing something wrong or have the alfer, given Sandi the wrong information?

 
GuyBarry
1318510.  Thu Apr 04, 2019 5:11 am Reply with quote

31 appears to be correct. Here's a diagram:

https://oeis.org/A000127/a000127.jpg

More terms in the sequence are given here:

Maximal number of regions obtained by joining n points around a circle by straight lines

So for 7 points it's 57 regions, for 8 it's 99 and for 9 it's 163.

 
suze
1318563.  Thu Apr 04, 2019 11:44 am Reply with quote

Trying to count the 31 regions on the illustration to which Guy links was making my head explode, so I've made a very crude one all of my own:




I'm going to guess that it doesn't have to be a circle. Would the 1, 2, 4, 8, 16, 31 ... sequence in fact work for any plane figure we cared to draw?

 
Lucas
1329122.  Sat Aug 31, 2019 11:55 am Reply with quote

not related but does anyone know who invented the car

 
crissdee
1329125.  Sat Aug 31, 2019 1:52 pm Reply with quote

For the genesis of the car as we know it, the usual answer is Karl Benz in 1885, but Joseph Cugnot built a steam powered wagon in (iirc) 1769.

 
Lucas
1329143.  Sun Sep 01, 2019 9:19 am Reply with quote

that was the point I was getting to but both benz's and cougnat's inspiration came around in a similar way, do you know how?

 
crissdee
1329157.  Sun Sep 01, 2019 4:19 pm Reply with quote

Couldn't afford a horse and tired of pushing?

 
Celebaelin
1329166.  Sun Sep 01, 2019 6:52 pm Reply with quote

31? For 6 points on a circle's circumference?

Does that work for a Star of David in a circle?



No. (13)

What conditions are being used? Oh hang on... maximal!. btw Isn't that a biological term? Shouldn't everyone else be saying it should be maximum?

So is there anything similar about minimal numbers in that regard; or perhaps minimum numbers?

 
suze
1329167.  Sun Sep 01, 2019 7:13 pm Reply with quote

Apparently maximal and maximum don't mean the same thing in mathematics.

As formally expressed, the difference between them looks a bit technical for my limited math knowledge. But at a basic level maximum means "everything else is smaller" while maximal means "nothing else is bigger". So if there are tied largest values there is no maximum, but the tied largest values are maximal.

 

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