Euclidean geometry | Discrete geometry | Polyhedra | Mathematical problems | Geometric dissection | Polytopes | Polygons
In geometry, a dissection problem is the problem of partitioning a geometric figure (such as a polytope or ball) into smaller pieces that may be rearranged into a new figure of equal content. In this context, the partitioning is called simply a dissection (of one polytope into another). It is usually required that the dissection use only a finite number of pieces. Additionally, to avoid set-theoretic issues related to the Banach–Tarski paradox and Tarski's circle-squaring problem, the pieces are typically required to be well-behaved. For instance, they may be restricted to being the closures of disjoint open sets. The Bolyai–Gerwien theorem states that any polygon may be dissected into any other polygon of the same area, using interior-disjoint polygonal pieces. It is not true, however, that any polyhedron has a dissection into any other polyhedron of the same volume using polyhedral pieces (see Dehn invariant). This process is possible, however, for any two honeycombs (such as cube) in three dimension and any two zonohedra of equal volume (in any dimension). A dissection into triangles of equal area is called an equidissection. Most polygons cannot be equidissected, and those that can often have restrictions on the possible numbers of triangles. For example, Monsky's theorem states that there is no odd equidissection of a square. (Wikipedia).
Practice Problem: Titration Calculations
Titration is a way to do stoichiometry with acids and bases. The equivalence point tells us something about the moles of acid and base that are present in solution at that moment. And if we know one of those values, we can know the other. Let's calculate some unknown concentrations! Try a
From playlist General Chemistry Practice Problems
Physics - Optics: Single Slit Diffraction (6 of 15) What Causes Intensity Diffraction Patterns?
Visit http://ilectureonline.com for more math and science lectures! In this video I will conceptually explain the intensity cause by diffraction patterns. Next video in series: http://youtu.be/OuaPzAN67fw
From playlist PHYSICS 61 DIFFRACTION OF LIGHT
Practice Problem: Analyzing Acid-Base Equilibria
Acids! Bases! Conjugate acids! Conjugate bases! We definitely have to be able to label such things, and we should also know how to state which direction in an acid-base equilibrium is preferred. To do this we should know how to tell which acid is stronger, and to do that we have to underst
From playlist Organic Chemistry Practice Problems
Light and Optics 8_5 The Diffraction Grating
The diffraction grating.
From playlist Physics - Light and Optics
Light and Optics 8_6 The Diffraction Grating
The diffraction grating.
From playlist Physics - Light and Optics
Practice Problem: Vicinal Dihalide Synthesis
We've got two vicinal dihalides with different stereochemistry, and we want to make them. How can we do this? Think about the reactions you know and give it a try! Try all of the organic chemistry practice problems: http://bit.ly/ProfDaveOCPP Organic Chemistry Tutorials: http://bit.ly/Pr
From playlist Organic Chemistry Practice Problems
Dangers of Dihydrogen Monoxide - The Less You Know 297
To learn how you can help in the fight against Dihydrogen Monoxide check out http://www.stevespanglerscience.com/dhmo.html
From playlist April Fool's Day Favorites
10% Students Solve This Trig Equation Wrong (Including me!)
Once you have a solid idea for how to solve trigonometric equations it is time for a challenge. A problem that will test you knowledge and ability to apply algebraic concepts to trigonometric equations. This problem does exactly that. ✅ Know when to use identities https://youtu.be/UArTc
From playlist Challenged and Confused Videos
MIT 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Fall 2012 View the complete course: http://ocw.mit.edu/6-849F12 Instructor: Erik Demaine This class focuses on hinged dissections. Examples of hinged dissections and several built, reconfigurable applications are offere
From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012
How to solve a double slit diffraction problem
In this video I show you how. to use the diffraction formula for the double slit diffraction situation. See www.physicshigh.com for all my videos and other resources. If you like this video, please press the LIKE and SHARE with your peers. And please add a COMMENT to let me know I have he
From playlist Nature of Light
Turning Circles to Squares: Equidecomposability and Dissection Puzzles
My submission for 3Blue1Brown's Summer of Math Exposition (SoME1) competition. This video deals with dissections of polygons and more general 2-dimensional shapes. A multimedia delve into the millennia-old problem. The DIY dissection puzzle (triangle to square) mentioned in the video can
From playlist Summer of Math Exposition Youtube Videos
Donald Bell - Loyd Polyominoes - G4G13 April 2018
Design of an 8-pience dissection of all the pentominoes to all of the tetrominoes.
From playlist G4G13 Videos
Hierarchical Interpolative Factorization
At the 2013 SIAM Annual Meeting, Lexing Ying of Stanford University discussed some recent results on developing new factorizations for matrices obtained from discretizing differential and integral operators. A common ingredient of these new factorizations is the interpolative decomposition
From playlist Complete lectures and talks: slides and audio
What is an aortic dissection? | Circulatory System and Disease | NCLEX-RN | Khan Academy
Created by Vishal Punwani. Watch the next lesson: https://www.khanacademy.org/test-prep/nclex-rn/rn-cardiovascular-diseases/rn-aortic-dissection-and-aneurysm/v/thoracic-aortic-aneurysms?utm_source=YT&utm_medium=Desc&utm_campaign=Nclex-rn Missed the previous lesson? https://www.khanacadem
From playlist Circulatory system diseases | NCLEX-RN | Khan Academy
Noether - Problems I Enjoy (1 of 3: General strategies)
More resources available at www.misterwootube.com
From playlist Mathematical Exploration
Aortic dissection treatment | Circulatory System and Disease | NCLEX-RN | Khan Academy
Created by Vishal Punwani. Watch the next lesson: https://www.khanacademy.org/test-prep/nclex-rn/rn-cardiovascular-diseases/rn-aortic-dissection-and-aneurysm/v/aneurysm-treatment?utm_source=YT&utm_medium=Desc&utm_campaign=Nclex-rn Missed the previous lesson? https://www.khanacademy.org/t
From playlist Circulatory system diseases | NCLEX-RN | Khan Academy
Scott Kim - Motley Dissections - G4G13 April 2018
This talk discusses motley dissections — polygons cut into polygons and polyhedra cut into polyhedra such that no two pieces every completely share an edge or a face. The most famous motley dissection is the squared square. My contribution extends this to triangled triangles, pentagoned pe
From playlist G4G13 Videos
Bolei Zhou - From Network Dissection to Policy Dissection: Emergent Concepts in Deep Representations
Recorded 9 January 2023. Bolei Zhou of the University of California, Los Angeles, presents "From Network Dissection to Policy Dissection: Discovering Emergent Concepts in Deep Representations" at IPAM's Explainable AI for the Sciences: Towards Novel Insights Workshop. Abstract: When the d
From playlist 2023 Explainable AI for the Sciences: Towards Novel Insights
Practice Problem: Gravimetric Analysis
What the heck is gravimetric analysis? Well let's say we want to know how much of a substance is in some mixture. We could toss it in solution and cause it to form a precipitate with some other ion in solution. We can measure the mass of that precipitate, and use that to find out how much
From playlist General Chemistry Practice Problems