User:Danenberg
Provenance
Of Gens Danenbergorum; Peter Charles Danenberg, Jr.
Officium
MediaWiki Development; namely WikiTeX
Sandbox
Direction field
Reproduced from William E. Boyce and Richard C. DiPrima, Elementary Differential Equations and Boundary Problems (Hoboken: John Wiley, 2005), 35.
Vector field
Gradient vector field of along with its contour map, courtesy of a beautiful hack by Thomas Sefzick.
Tangent planes
At increasing levels of detail, the surface approaches its tangent plane around P.
Falling leaf
Anti-intuition
Linear independence
Problem
If for
, show that
is linearly independent on every interval for all fixed
.
Wronskian
Solution
has a non-zero Wronskian on
; and is therefore linearly independent on that interval.
Clairaut's Theorem
That does not contradict Clairaut's Theorem
, where
and
are permuted indices of
with replacement, since
and
are not continuous.
Violent curiosity
Tangent at a point of plane-ellipsoid intersection:
Partial derivatives
Limit
That--doesn't-exist's graphical representation.
Family of curves
Curve with contour
Erotic paraboloid
Context from #math on freenode:
00:57 <klutometis> I've come up with a new nomination: the "erotic paraboloid" 00:57 <klutometis> http://wikisophia.org/wiki/User:Danenberg#Erotic_paraboloid 00:58 <thermoplyae> you appear to have a lot of free time 00:59 <klutometis> thermoplyae: me? it corresponds roughly with calculus; so no expenditure of free time 00:59 <TRWBW> klutometis: hehe, n1, something just like it at http://www.youtube.com/watch?v=eBGIQ7ZuuiU 01:00 <thermoplyae> you say that, but all the busy people i know don't draw graphs of "co-sinusoidal demi-toroid"s 01:00 <klutometis> damn it, TRWBW; I can't believe I got rick rolled 01:00 <thermoplyae> just sayin' 01:00 <thermoplyae> haha 01:01 <klutometis> thanks, boys; good night
Osculating cirles
Tangent, normal, binormal
Curvature of e
<t, t², t³> ∩ <sin(t), sin(2t), t>
Cylinder ∩ paraboloid
Co-sinusoidal demi-toroid
Toroidal spiral
Orthogonal matrices
Problem
Inverse matrix
Solution
Surfaces
Fugale Gelehrtheit
Index conjecture
Let be the index set to the n-ary Cartesian product of set
of cardinalities
. Therefore,
; let
.
Let, furthermore, be the index of set
corresponding to
.