Framerate synced with a bird’s wings
With 9s we can produce another aesthetically pleasing pattern shown below.
999,999 · 1 = 0,999,999
999,999 · 2 = 1,999,998
999,999 · 3 = 2,999,997
999,999 · 4 = 3,999,996
999,999 · 5 = 4,999,995
999,999 · 6 = 5,999,994
999,999 · 7 = 6,999,993
999,999 · 8 = 7,999,992
999,999 · 9 = 8,999,991
999,999 · 10 = 9,999,990
Here is another number pattern, where the number 9 is multiplied by a number representing the consecutive natural numbers- increasing by 1 each time- and then added to the initial natural numbers consecutively.
0 · 9 + 1 = 1
1 · 9 + 2 = 11
12 · 9 + 3 = 111
123 · 9 + 4 = 1111
1234 · 9 + 5 = 11111
12345 · 9 + 6 = 111111
123456 · 9 + 7 = 1111111
1234567 · 9 + 8 = 11111111
12345678 · 9 + 9 = 111111111
We can consider number patterns that can be generated in a similar fashion, yet somewhat in the reverse of the previous one. However, this time the generated number consist of all 8s.
0 · 9 + 8 = 8
9 · 9 + 7 = 88
98 · 9 + 6 = 888
987 · 9 + 5 = 8888
9876 · 9 + 4 = 88888
98765 · 9 + 3 = 888888
987654 · 9 + 2 = 8888888
9876543 · 9 + 1 = 88888888
98765432 · 9 + 0 = 888888888
Now that we have introduced the 8s in a rather dramatic fashion, we shall use them as the multiplier with the numbers consisting of increasing natural numbers, and each time adding successive natural numbers. Appreciating the number pattern shown here is more pleasing than trying to explain this phenomenon, which could conceivably detract from its beauty.
1 · 8 + 1 = 9
12 · 8 + 2 = 98
123 · 8 + 3 = 987
1234 · 8 + 4 = 9876
12345 · 8 + 5 = 98765
123456 · 8 + 6 = 987654
1234567 · 8 + 7 = 9876543
12345678 · 8 + 8 = 98765432
123456789 · 8 + 9 = 987654321
Content credit: Mathematical Curiosities A Treasure Trove of Unexpected Entertainment
Survival Tips For Your Life
Just a reminder that I do have an etsy store with Legacy of Kain neckwarmers and badges, dragon age neckwarmers and bracelets, and all my Batman Illusion scarves!
Www.etsy.com/shop/polkadotnerd
I have a ton of expenses coming up soon, so reblogs are encouraged and appreciated!
LEGO Nautilus, Ammonite, and Trilobites
Created by Tim Goddard
The answer is NO, you can not. This is why all map projections are innacurate and distorted, requiring some form of compromise between how accurate the angles, distances and areas in a globe are represented.
This is all due to Gauss’s Theorema Egregium, which dictates that you can only bend surfaces without distortion/stretching if you don’t change their Gaussian curvature.
The Gaussian curvature is an intrinsic and important property of a surface. Planes, cylinders and cones all have zero Gaussian curvature, and this is why you can make a tube or a party hat out of a flat piece of paper. A sphere has a positive Gaussian curvature, and a saddle shape has a negative one, so you cannot make those starting out with something flat.
If you like pizza then you are probably intimately familiar with this theorem. That universal trick of bending a pizza slice so it stiffens up is a direct result of the theorem, as the bend forces the other direction to stay flat as to maintain zero Gaussian curvature on the slice. Here’s a Numberphile video explaining it in more detail.
However, there are several ways to approximate a sphere as a collection of shapes you can flatten. For instance, you can project the surface of the sphere onto an icosahedron, a solid with 20 equal triangular faces, giving you what it is called the Dymaxion projection.
The Dymaxion map projection.
The problem with this technique is that you still have a sphere approximated by flat shapes, and not curved ones.
One of the earliest proofs of the surface area of the sphere (4πr2) came from the great Greek mathematician Archimedes. He realized that he could approximate the surface of the sphere arbitrarily close by stacks of truncated cones. The animation below shows this construction.
The great thing about cones is that not only they are curved surfaces, they also have zero curvature! This means we can flatten each of those conical strips onto a flat sheet of paper, which will then be a good approximation of a sphere.
So what does this flattened sphere approximated by conical strips look like? Check the image below.
But this is not the only way to distribute the strips. We could also align them by a corner, like this:
All of this is not exactly new, of course, but I never saw anyone assembling one of these. I wanted to try it out with paper, and that photo above is the result.
It’s really hard to put together and it doesn’t hold itself up too well, but it’s a nice little reminder that math works after all!
Here’s the PDF to print it out, if you want to try it yourself. Send me a picture if you do!
Breakfast far above the clouds, Pokut, Turkey
Offering a showy Large Curled with eyes at base, on matrix, Phacops Spine Trilobite. From Mt. Issimour, Morocco, 350 million years 2.4 inch wide fossil only by 2 inches. Overall 3 inches tall by 2.5 inch wide. Shows all around, excellent coloration and professional prep. No spines missing.
www.etsy.com/shop/GoldenHourMinerals
http://stores.ebay.com/Golden-Hour-Fossil-and-Minerals www.goldenhourminerals.com
Positives of High Functioning Anxiety/Depression: I can complete day-to-day tasks
Negatives of High Functioning Anxiety/Depression: Literally nobody has any sympathy for you when you’re depressed or having panic attacks because you’re so fine most of the time.