Blender Open Material Repository - download blender materials/shaders for free!
What does 0^0 (zero raised to the zeroth power) equal? Why do mathematicians and high school teachers disagree
Clever student: I know! Now we just plug in x=0, and we see that zero to the zero is one! Cleverer student: No, you’re wrong! which is true since anything times 0 is 0. Cleverest student : That doesn’t work either, because if then is so your third step also involves dividing by zero which isn’t allowed! and see what happens as x>0 gets small. So, since = 1, that means that High School Teacher: Showing that approaches 1 as the positive value x gets arbitrarily close to zero does not prove that . is undefined. does not have a value. Calculus Teacher: For all , we have Hence, That is, as x gets arbitrarily close to (but remains positive), stays at On the other hand, for real numbers y such that , we have that That is, as y gets arbitrarily close to Therefore, we see that the function has a discontinuity at the point . but when we approach (0,0) along the line segment with y=0 and x>0 we get Therefore, the value of is going to depend on the direction that we take the limit. that will make the function ! . as is whatever
Carved Book Landscapes by Guy Laramee
(click images for detail) For the better part of three decades multidisciplinary artist Guy Laramee has worked as a stage writer, director, composer, a fabricator of musical instruments, a singer, sculptor, painter and writer. Among his sculptural works are two incredible series of carved book landscapes and structures entitled Biblios and The Great Wall, where the dense pages of old books are excavated to reveal serene mountains, plateaus, and ancient structures. Of these works he says: So I carve landscapes out of books and I paint Romantic landscapes. Laramee’s next show will be in April of 2012 at the Galerie d’Art d’Outremont in Montreal.
IED Visual Communication
Vi Hart: Math Doodling
Remember that video about doodling dragons and fractals and stuff? I finally finished part 2! Here is a magnet link so you can dowload it via torrent. Here it is on YouTube: You can tell I worked on it for a long time over many interruptions (travelling and other stuff), because in order to keep myself from hating what was supposed to be a quick easy part 2, I had to amuse myself with snakes. Here was part 1, via Torrent or YouTube.
Scientists Discover The Oldest, Largest Body Of Water In Existence--In Space
Scientists have found the biggest and oldest reservoir of water ever--so large and so old, it’s almost impossible to describe. The water is out in space, a place we used to think of as desolate and desert dry, but it's turning out to be pretty lush. Researchers found a lake of water so large that it could provide each person on Earth an entire planet’s worth of water--20,000 times over. The water is in a cloud around a huge black hole that is in the process of sucking in matter and spraying out energy (such an active black hole is called a quasar), and the waves of energy the black hole releases make water by literally knocking hydrogen and oxygen atoms together. The official NASA news release describes the amount of water as “140 trillion times all the water in the world’s oceans," which isn’t particularly helpful, except if you think about it like this. That one cloud of newly discovered space water vapor could supply 140 trillion planets that are just as wet as Earth is.
60 Free Illustrator Brushes
Adobe Illustrator has many powerful tools and unique features. And one among them is Illustrator's Paintbrush Tool (B). The brushes can be applied to paths and strokes, they are great for creating stunning stroked designs in seconds. And, the best part about Illustrator's brushes is that they are vectors and can be completely modified to suit your needs by changing their colors, stroke width, weight, and more. Introduction In this article, you will find a huge compilation of excellent and stunning sets of free Illustrator Brushes on the web, such as: floral flourishes, swirls, foliage brushes, sketch brushes, watercolor brushes, chains, ropes, beautiful border brushes, Christmas themes, snowflakes, beads, gem brushes, and more. You can find more about how to use brushes in Illustrator in our post titled, "A Comprehensive Guide: Illustrator's Paintbrush Tool and Brush Panel." Floral, Swirl and Foliage Brushes 1. A brush set to draw variety of flowers, it includes 8 of them. 2. 5. 6. 7. 8.
Weierstrass functions
Weierstrass functions are famous for being continuous everywhere, but differentiable "nowhere". Here is an example of one: It is not hard to show that this series converges for all x. Here's a graph of the function. You can see it's pretty bumpy. Below is an animation, zooming into the graph at x=1. Wikipedia and MathWorld both have informative entries on Weierstrass functions. back to Dr.
Scientists Create Material More Insulating than the Vacuum
(PhysOrg.com) -- With its complete lack of atoms, a vacuum is often considered to be the best known insulator. For this reason, vacuums are regularly used to reduce heat transfer, such as in the lining of a thermos to keep beverages hot or cold. However, in a recent study scientists have found a material even less able to conduct heat: a stack of photonic crystals layered within a vacuum can create a material with a thermal conductance just half that of empty space alone. Basically, heat can be transferred from one material to another in three main ways: convection, conduction, and radiation. Conduction and convection both require some kind of material medium for heat to pass through; therefore, the lack of material in a pure vacuum greatly minimizes the effectiveness of these two processes. However, heat can also be transferred through infrared radiation, a form of light that is invisible but can be felt as heat. More information: W T Lau et al.
Tutorials
Beginner GIMP Quickies Use GIMP for simple graphics needs without having to learn advanced image manipulation methods. Simple Floating Logo This tutorial walks through some basic image and layer manipulation techniques. Layer Masks An introduction to using layer masks to modify the opacity of a layer. Basic Color Curves A first look at the Curves tool and adjusting color tones in an image. Photo Editing Digital B&W Conversion Detailed conversion tutorial for generating a B&W result from a color image. Luminosity Masks Using multiple layer masks to isolate specific tones in your image for editing. Tone Mapping with ‘Colors/Exposure’ Using high bit depth GIMP’s ‘Colors/Exposure’ operation to add exposure compensation to shadows and midtones while retaining highlight details. Programming Basic GIMP Perl Learn how to write simple perl scripts using the gimp-perl module (GNU/Linux users only). Automate Editing Using GIMP Python to automate a workflow. All (Legacy) Tutorials List
FanWing
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