#semiperfect

[tomasvall]

Nobody’s truly perfect, not even cell . . . . . . . . . This is such a cool design but very hard to nail down how much you can flex with his “look” before it’s no longer cell. Will upload a lot of sketches that led up to this drawing later. . . . . . . . . #cell #imperfect #dragonball #fighterz #dragonballsuper #villain #watercolor #bic #alien #horror #perfect #semiperfect #action #comics #tomasvall #illustration

[pokexhibit]

a (rather quick) semi for @ronkeydrawsdb, from a while ago

ah yes, back at it again with making scary vilians be colorful and lively and i blame her for this one specifically 

[goldsmall]

What I have been doing for the last week:

MTH 210 Just Right Problem

When a set "number of terms" value is found will those numbers have a pattern or relationship between them?

Introduction:

In class we had an example where sequences of consecutive positive integers added up to the number 90. We were given four different sequences, and in class we found 2 more. I was looking to further explore how many sequences of consecutive integers could be found to add to 90, while noting the median number and how many numbers are in the sequence.

What I found:

I found that there are 12 sets of sequences of consecutive numbers that when summed equal 90. Using only positive integers the sequences are:

1: 90

3: 29,30,31

4: 21,22,23,24

5: 16,17,18,19,20

9: 6,7,8,9,10,11,12,13,14

12: 2,3,4,5,6,7,8,9,10,11,12,13

Using negative and positive integers the additional sequences are:

15: -1,0,1,...,13

20: -5,-4,-3,-2,-1,0,1,2...,14

36: -15,-14,-13,...,0,...,18,19,20

45: -20,-19,-18,...,0,...,22,23,24

60: -28,-27,-26,...,0,...,20,30,31

180: -89,-88,-87,...,0,...,88,89,90

Where the numbers on the left of the colon are the numbers of terms in the sequence. These sequences were found by taking 90 and dividing it by x and producing a number y. If 2y is a whole number then y would be the median of the sequence and x was how many numbers are in the sequence.

So with all the sets of sequences found, I took all the "number of numbers in a sequence" and made and listed them in a new set: 1,3,4,5,9,12,15,20,36,45,60,180

When looking at this set if you take two numbers, each number from the opposite end of the set, when multiplied they total 180.

Examples: 1*180=180, 3*60=180, 4*45=180, ect

180 is significant to me because it's the highest number of numbers in a sequence, also 90*2=180 I think that my set of numbers is complete because this pattern exists. Though this only one set, so to explore this more I did the same things for the number 40, which was picked because 40, like 90, is a semi-perfect number. Furthermore 40 is not a divisor of 90 so I figured it was a good outside example.

40 only had two sets of sequences using only positive integers.

1: 40

5: 6,7,8,9,10

Additionally two more were obtained using positive and negative integers:

16: -5,-4,-3,-2,-1,0,1,...,10

80: -39,-38,-37,...,-1,0,1,...,38,39,40

Looking at this solution set of 1,5,16,80, it is easy to see that by multiplying the outside numbers, 1*80=80, and when you multiply the inside numbers, 5*16=80.