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Four-dimensional space
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1	COMMON TANGENTS TO FOUR UNIT BALLS IN R3 ´ IAN G. MACDONALD, JANOS PACH, AND THORSTEN THEOBALD Abstract. We answer a question of David Larman, by proving the following result. Any four unit balls in 3-dimensional space, Add to Reading List Source URL: www.math.uni-frankfurt.de Language: English - Date: 2014-01-06 16:44:48 Geometry Convex geometry Graph theory Deltahedra Platonic solids Algebraic curve Tetrahedron
2	A MATRIX–BASED PROOF OF THE QUATERNION REPRESENTATION THEOREM FOR FOUR-DIMENSIONAL ROTATIONS arXiv:math/0501249v1 [math.GM] 16 Jan 2005 Add to Reading List Source URL: arxiv.org Language: English - Date: 2008-02-01 16:08:31 Quaternions Rotations in 4-dimensional Euclidean space Quaternions and spatial rotation Rotation matrix Versor Rotation Matrix Orthogonal matrix Orientation Rotation formalisms in three dimensions Charts on SO
3	IGL Project Report∗ Applications of n-dimensional Integrals: Random Points, Broken Sticks and Intersecting Cylinders A.J. Hildebrand (Faculty Mentor)† Lingyi Kong, Abby Turner, Ananya Uppal (Undergraduate Members) Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2012-12-12 13:44:20 Surfaces Dimension Elementary geometry Spheres Steinmetz solid Cylinder Integral Three-dimensional space Four-dimensional space Area N-sphere Two-dimensional space
4	Preface to Shadows of Reality, The Fourth Dimension in Relativity, Cubism, ad Modern Thought A Yale University Book, 2006 We walk in the here and now, but is there a space beyond, a space that impinges on our own infinit Add to Reading List Source URL: tonyrobbin.net Language: English - Date: 2013-03-03 09:18:07 Projective geometry Four-dimensional space Dimension Homography Geometry Point at infinity Homogeneous coordinates Space Projection Planar projection Hyperbolic geometry
5	NUCLEAR PHYSICS AND ELEMENTARY PARTICLES QUANTUM-CONSISTENT SUPERSTRING MODELS IN FOUR DIMENSIONAL SPACE-TIME A.J. Nurmagambetov∗ National Science Center ”Kharkov Institute of Physics and Technology”, 61108, Khark Add to Reading List Source URL: vant.kipt.kharkov.ua Language: English - Date: 2009-10-19 05:37:56 Superstring theory Supergravity Compactification Bosonic string theory M-theory Superspace Membrane Brane cosmology Supersymmetry Physics Quantum field theory String theory
6	Thirteen?? David Mumford A large part of what a mathematician does may be described as exploring “things” which they discover through reasoning, which become as real to them as the house they live in but which have n Add to Reading List Source URL: www.gregkucera.com Language: English - Date: 2015-01-07 20:36:16 Moduli theory Invariant theory Moduli space Special relativity Space Four-dimensional space Moduli of algebraic curves Category of being Line bundle Mathematics Dimension Geometry
7	ABHINAV NATIONAL MONTHLY REFEREED JOURNAL OF RESEARCH IN SCIENCE & TECHNOLOGY www.abhinavjournal.com A METHOD FOR TRACKING OF ENEMY OR Add to Reading List Source URL: www.abhinavjournal.com Language: English - Date: 2014-01-30 00:14:00 Electromagnetic radiation Virtual reality 3D computer graphics Camera lens Real image Ray tracing Lens Three-dimensional space Four-dimensional space Optics Geometrical optics Atomic molecular and optical physics
8	Physics on a Branched Knotted Spacetime Manifold C. Ellgen⇤ and G. Biehle (Dated: March 2, 2015) Abstract This paper reproduces the dynamics of quantum mechanics with a four-dimensional spacetime Add to Reading List Source URL: knotphysics.net Language: English - Date: 2015-03-02 18:51:06 Lorentzian manifolds Differential topology Relativity Geometric topology Manifold Ricci curvature Spacetime Minkowski space Metric tensor Physics Theoretical physics Topology
9	DOC Document Add to Reading List Source URL: www.gresham.ac.uk Language: English - Date: 2014-12-10 11:17:15 9 Four-dimensional space Geometry Mathematics The nature of God in Western theology So Plastic So Pretty Philosophy Dimensional analysis Measurement
10	16th Canadian Conference on Computational Geometry, 2004 On the number of line tangents to four triangles in three-dimensional space Add to Reading List Source URL: www.cccg.ca Language: English - Date: 2004-08-23 15:27:23 Tangent Triangle Hyperbola Trigonometric functions Tangent lines to circles Homothetic center Geometry Analytic geometry Conic section

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