Paper folding | Area | Polyhedra | Mathematical paradoxes
In mathematics, the Schwarz lantern is a polyhedral approximation to a cylinder, used as a pathological example of the difficulty of defining the area of a smooth (curved) surface as the limit of the areas of polyhedra. It is formed by stacked rings of isosceles triangles, arranged within each ring in the same pattern as an antiprism. The resulting shape can be folded from paper, and is named after mathematician Hermann Schwarz and for its resemblance to a cylindrical paper lantern. It is also known as Schwarz's boot, Schwarz's polyhedron, or the Chinese lantern. As Schwarz showed, for the surface area of a polyhedron to converge to the surface area of a curved surface, it is not sufficient to simply increase the number of rings and the number of isosceles triangles per ring. Depending on the relation of the number of rings to the number of triangles per ring, the area of the lantern can converge to the area of the cylinder, to a limit arbitrarily larger than the area of the cylinder, or to infinity—in other words, the area can diverge. The Schwarz lantern demonstrates that sampling a curved surface by close-together points and connecting them by small triangles is inadequate to ensure an accurate approximation of area, in contrast to the accurate approximation of arc length by inscribed polygonal chains. The phenomenon that closely sampled points can lead to inaccurate approximations of area has been called the Schwarz paradox. The Schwarz lantern is an instructive example in calculus and highlights the need for care when choosing a triangulation for applications in computer graphics and the finite element method. (Wikipedia).
World's Most Powerful Visible Diode Laser
"The NUBM44 Laser Diode" The World's Most Powerful
From playlist Lasers
If I could only glow from my whole body... heh, now I can. Glowstick Glowman Costume. www.NothingButCostumes.com
From playlist Amazing Stuff
Nernst Lamp (Nernst Glower) was developed in 1897 as a more efficient replacement for Edison's incandescent lamp. Lighting collector Rick DeLair takes you through all the parts of the Nernst Lamp. See schematics, heater tubes, glower, shifter, ballast. First sold by AEG 1900, and Westingho
From playlist Lighting Technology
A Liter Of Light *Official Version*
Check out this mini-docu that we shot! http://www.playwiththejunglegym.com/
From playlist Amazing Stuff
Laser sind überall: in CD- und DVD-Playern, Supermarkt-Scannern und Druckern. Aber was unterscheidet Laserlicht eigentlich von herkömmlichen Glühlampen und wie entsteht es? Dabei dreht sich alles um die Anregung von Elektronen mit Energie. Material für die Schule: Techmax 06: Laser https:
From playlist Most popular videos
Black Hole Apocalypse — Official Trailer
Join astrophysicist Janna Levin and others as they hunt for clues about the nature of black holes. NOVA’s “Black Hole Apocalypse” premieres January 10 on PBS. NOVA on Facebook: https://www.facebook.com/NOVAonline NOVA on Twitter: @novapbs NOVA on Instagram: @novapbs
From playlist Previews
FRESNEL LENS FIBER OPTIC OPTICAL CABLE Solar Lighting
This is a Spot Fresnel Lens focused on composite Fiber Optic Cable. This is a fiber optic ponytail.
From playlist THE FRESNEL LENS SOLAR POWER
Navigate fields of cosmic objects in your quest to become a black hole. The NOVA Black Holes App is available free from the App Store on iPad or at https://itunes.apple.com/us/app/nova-black-holes/id1114574985
From playlist Original shorts
The Illuminating History of the Jack-o-Lantern
It is October, and millions of American children will be participating in an annual tradition, traveling to a local pumpkin patch to choose the orange orb that they and their parents will carve into a Jack-o-Lantern. But where did the entire idea arise? And how long has it been going on?
From playlist Halloween with the History Guy
The History of Jack O' Lanterns
With Halloween approaching, we're entering into many peoples favorite time of year. From the free candy to the spooky decorations, Halloween has become a night to have fun for many across the world. Many people's favorite activity is carving pumpins into Jack o' lanterns, but why are they
From playlist Concerning History
Lantern Walk remains one of ASU's oldest and most treasured traditions. It was first celebrated in 1917. Each year students, alumni, faculty, staff and friends climb to the top of A Mountain carrying lanterns to light up Tempe, following in the footsteps of their Sun Devil ancestors. At
From playlist ASU Now
The Bridge Riddle | Don't Memorise
In this riddle (which is inspired by the TED-Ed bridge riddle), can you help Nora and her family cross the bridge? Also, can you answer the follow-up question asked at the end of the video? 0:00 Question 1:29 Understanding the Clues 2:50 Strategies 5:40 Solution 8:08 Follow-up riddle To
From playlist Riddles/Puzzles/Brain Teasers
3. Lighting; Trip Introduction
MIT SP.775 D-Lab Energy, Spring 2011 View the complete course: http://ocw.mit.edu/SP-775S11 Instructor: Amy Banzaert License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT SP.775 D-Lab: Energy, Spring 2011
A Kerosene Lantern... Bioreactor?
Bioreactors are very simple, but extremely useful devices. They're basically a large tank that microorganisms can be grown in, but what makes them special is their ability to grow a nearly infinite amount of the organism or a product an organism produces by slowly feeding in fresh nutrient
From playlist Biology and Genetics
The Coolest Stuff on the Planet - The Akita Kanto Festival
The Kanto Festival in Akita City, Japan, is a harvest festival famous for music, parades, chanting -- and men balancing giant poles of lanterns on various parts of their bodies. Discover why the Kanto Festival is Cool Stuff in this episode.
From playlist The Coolest Stuff on the Planet
The Fluorescent Lamp - How it Works - Inventors
Introduction to fluorescent lamps: How it works, inventors, animations. The fluorescent light is the most prolific type of lamp in the world. For indoor lighting it remains the lowest cost efficient light source. Inventors include George Inman, Richard Thayer, Edmund Germer, Albert Hull, E
From playlist Fluorescent Lamp Videos
Next live stream is tomorrow at 7PM EST In this live stream we go in search of Momma Beehive, a severed arm and in the process we find two awesome guns!!! Thank you to everyone that joins me for these live streams. They are a ton of fun and they give me a chance to play an awesome game an
From playlist Live Stream Gaming
Can you solve the bridge riddle? - Alex Gendler
View full lesson: https://ed.ted.com/lessons/can-you-solve-the-bridge-riddle-alex-gendler Want more? Try the buried treasure riddle: https://www.youtube.com/watch?v=tCeklW2e6_E Taking that internship in a remote mountain lab might not have been the best idea. Pulling that lever with the
From playlist Bridge Building
What's Behind The Firefly's Glow | What's Inside?
The firefly is probably the Earth’s most famous bioluminescent species, with over 2,000 individual species. And the secret to its light comes from two essential components: luciferin and luciferase. But while the firefly may have evolved its lantern as a form of protection, today the light
From playlist Animal Science
Teach Astronomy - Speed of Light
http://www.teachastronomy.com/ Light and all other forms of electromagnetic radiation travel at 300 thousand kilometers per second or 186 thousand miles per second. This is the speed of light denoted by the small letter "c". The speed of light is so fast that it was not possible to measu
From playlist 05. Quantum Theory and Radiation