DateString[]

Recitation Week 6-9 Sept.

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Something interesting

This is a section

tux = Graphics3D[Sphere[]]

alpha = Sin[Pi/6]

Sin[tux]

Integrate[tux^2,tux]

corners[1] = {1,0,0};
corners[2] = {0,1,0};
corners[3] = {0,0,1};
corners[4] = {1,1,0};
corners[5] = {1,0,1};
corners[6] = {0,1,1};
corners[7] = {0,0,0};
corners[8] = {1,1,1};

radius = 1/3

Graphics3D[
{Blue,
Sphere[corners[1],radius],
Sphere[corners[2],radius],
Sphere[corners[3],radius],
Sphere[corners[4],radius],
Sphere[corners[5],radius],
Sphere[corners[6],radius],
Sphere[corners[7],radius],
Sphere[corners[8],radius]

}
]

Table[i,{i,6}]

listOfSpheres = Table[
Sphere[corners[i],radius],
{i,1,8}]

Graphics3D[listOfSpheres]

faceCenter[1] = {1,1,0}/2

fccPart1 = Permutations[faceCenter[1]]

fccPart2 = Permutations[{(1/2),(1/2),1}]

fcc = Join[fccPart1,fccPart2]

fcc[[3]]

fccSpheres =  Table[
Sphere[fcc[[i]],1/3],
{i,1,6}]

gFCC = Graphics3D[fccSpheres]

gCorners = Graphics3D[{Blue,listOfSpheres}]

Show[{gCorners,gFCC}]

Manipulate[
Graphics3D[{Sphere[],Cylinder[{{0,0,0},{a,0,0}},.1],Sphere[{a,0,0}]}],
{a,1,6}]

Different kinds of equals signs...

simple assigment

theLeftHandSide = Pi/12

Logical equals ==

Sam== theLeftHandSide

Delayed Assignment (Don’t assign until the variable is used....) :=

aTime = DateString[]

aTime

theTime := DateString[]

Table[Pause[1];theTime,{i,1,10}]

Table[Pause[1];aTime,{i,1,4}]

Solving Equations

Clear[x,a,b,c]

theLHS = a x^2 + b x + c

theRHS = 0

theLHS

c+bx+(ax^2)

theRHS

theEquation = theLHS== theRHS

Solve[theEquation,x]

theSolA = Solve[theEquation,a]

theLHS

theLHS/.theSolA

theXSOLS = Solve[theEquation,x]

Simplify[theLHS/.theXSOLS]

Introducing new symbol  /.    This means apply the following rule....  and a rule is defined by a -> b

list = { 2 a , 3 b a, a, b, a-b}

list/.a-> 1

list/.a-> b