Geometer's Sketchpad Done & Old Stuff

Notes & TOC Listed by Focus Listed Alphabetically Old Stuff GSPfa21.htm

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Summer 2021 - Fall 2023 New Stuff
Backstory webpage

Fall 2024 Sketch Pad and Other Stuff

Sine Law
Digital Manipulative with Sketchpad
1st: Input A and a and b.
2nd: The givens are drawn.
3rd: Rotate segment a to solve the triangle by placement of point B.
4th: Dimensions B, C, and c are stated.
5th: The closer the sum is to 180 degrees, the better the estimates.
Also:
Concrete Representation
Digital Manipulative with Excel
Solve Triangle Computation

Before Precalc

line -- line segment by dragging & by coordinates, midpoint, distance formula, point-slope equation, perpendicular, parallel lines
-- slide points A and B and generate equation of the line in 4 forms.
-- computes slopes and writes lines by sliding and by parameters
1 - drag segment endpoints to compute midpoint and distance
2 - show how the distance formula computes
3 - find a perpendicular w/input coordinates
4 - find parallel w/input coordinates
2graphs.gsp -- 1,2 graphed functions, piece-wise, composite ready to edit, link to "coordinate" and more history, table of f(x) gps files
make.hexagon.gsp -- construct a hexagon, and also consider other polygons w/a look towards pi

Functions, Lines, Circles

Cartesian -- definition and analytic history web page
ssong.gsp -- slope from history, to sound, to words & numbers, through examples, to computation
0 - toc, history
1 - only 1 function
2 - parabola w/tangent line
3 - cubic w/tangent line
4 - polynomial
5 - rational
6 - compute slope drag 2 points
7 - dy/dx by definition
8 - m= given A, B
9 - 3 points define a parabola
10 - notes on 3 points define a parabola
circle.tangent.normal.gsp
1 drag center & radius 2 create equation
2 enter h, k, r
3 perpendicul w/input coordinates
4 slide tangent then compute & write
circleFormula.gsp --
inverse.gsp
0 - vertical, horizontal line tests
1 - square root fx
2 - any function
3 - sqrt fx by parameters
4 - restricted domain on inverse
5 - arcsine
6 - arctangent
7 - f and inverse
8 - f, inverse, tangents --

Polynomial and Rational Functions

compositeFX.gsp --
parabola.gsp --
compositeFx.poly.ratl.gsp
0 - graph of 1 function
1 - graphs of 2 functions
2 - composite of 4 functions
3 - polynomial. links to polynomial, dilations gif, quatratic.htm, equation, discriminant
4 - rational, rational function features & how to find them
5 - end behavior, battle of (Ax^m)/(Bx^n)

Right Triangle & Trig

standardPosition.gsp
1 standard position angle central angle, negative & positive angle measures
2 angles coterminal?
radianSector.gsp
1 intro angles degrees radians
2 radian questions
3 arc length angular speed sector area
4 sector and area
veronica.gsp
1 - 1 standard position angle
2 - angles coterminal?
3 - 1 veronica angles -- trig fx of angles is 4 quadrants
4 - 2 veronica angles
5 - extra 2 veronica angles
elevation.gsp - angle of elevation, depression, ladders w/h(x), y(x), and h(y), x(y), and h as variable, and h s a constant

Calculus

Limits

limit -- limit by epsilon-delta, by dragging x, by approach from L & R, by table
0 -The Modern Evolution of Limit and Its Symbols
1 - approach by dragging x
2 - by above & below x
3 - table of x, f(x), f'(x), f''(x) w/tangent line
4 - limit, as x goes to infinity, (Ax^m)/(Bx^n) battle pix, emd behavior
5 - limit as h goes to 0, derivative by limit of difference quotient
6 - by solpe of secant
7 - webpage sample epsilon-delta
8 - simple sample limit questions
9 - by epsilon-delta
10 - Squeeze to take a limit, link to proof Dx(sin(x) = cos(x)
limh4Dx.gsp
limitWquestions.gsp

Derivatives
Derivatives Web Page

Intro2AntiDerivative.gsp
0 - intro relation between sum and integral. Includes link to
http://www.mathnstuff.com/math/gsp/sumr19/su19newgsp/ReimannSums.gsp
0.5 - summary notation.
1 - partition
2 - subscript x0 start
3 - subscript x1 start
4 - left boxes n=4, x0
5 - Reimann sums
6 - see n [a,b]
7 - int(x) plus c
8 - by plotint(x) green dots
9 - extra - h(x) input [a,b]
DerAnyFx.gsp
1 - fx w/tangent line & tan line equation
2 - sqrt(x) & TRACE
3 - sqrt(x), tan, TRACE f '(x)
4 - EMOJI, x, fx, f'x f''x, tan line
5 - table, x, fx, f'x, f''x
emoji.gsp
0 - toc - Links to: dictionary, algebra notes, precalc notes, calc 1 notes
1 - f' by tangent, x, fx, f'x, f''x
2 - trig f' by tangent, x, fx, f'x, f''x
3 - polynomial
4 - rational
http://www.mathnstuff.com/math/gsp/sumr19/su19newgsp/fX.f'X.f''X.intX.dy.gsp
3
0 - resources including: derivative definition, calc cheat sheet, link to derivative calculator, link to integration calculator, derivative connect-the-dots, integration connecet-the-dots
1 - f'(x), tan line, TRACE f'(x), table
2 - Leibnitz, Newton pix
3 - limit as h goes to 0
4 - no table x, f(x), f'(x), f''(x), tangent line included
5 - build table x, f(x), f'(x), f''(x)
6 - hand-plot sums
7 - extra hand-plot
8 - auitomatic 2 fx plot
9 secant images, link to wikipedia
Mean.Rolle.f'(x).f''(x).gsp
0 - by secant & lim as h --> 0 of DQ
1 - fx w/tangent line
2 - just c on interval
3 - tan line f(x), f'(x), f''(x)
4 - f, f', TRACE, table
5 - sine emoji, w/tan & trace, f', f''
6 - fx tan & trace emoji, f f', f''
7 - Mean Value Theorem. slide [a,b]
8 - Roll's Theorem, slide [a, b]
9 - derivative tests, f, f', f'', emoji
10 - s(t), s'(t), s''(t), RED
11 - no table x, fx, f'x, f''x
12 - extra Rolle's
13 - x,f,f',f'',RIGHT&LEFT
tracef.f1.f2.f3.f4.gsp
DerAnyFx.gps -- Derivative of Any Function
* One may trace the function and see coordinates displayed.
* One may edit the function.
* One may graph the approximate derivative function.
1 - f(x) w/tangent line
2 - f(x) & TRACE
3 - any f(x): x, f(x), f'(x), f''(x)
4 - sin(x): x, f(x), f'(x), f''(x)
tracef.f1.f2.f3.f4.gsp
derivativeTests.gsp
DERlnx.gsp --
for related rates, use elevation.gsp - angle of elevation, depression, ladders w/h(x), y(x), and h(y), x(y), and h as variable, and h s a constant

Reimann Sums & Antiderivatives

Intro2AntiDerivative.gsp
0 - intro relation between sum and integral. Includes link to
http://www.mathnstuff.com/math/gsp/sumr19/su19newgsp/ReimannSums.gsp
0.5 - summary notation.
1 - partition
2 - subscript x0 start
3 - subscript x1 start
4 - left boxes n=4, x0
5 - Reimann sums
6 - see n [a,b]
7 - int(x) plus c
8 - by plotint(x) green dots
9 - extra - h(x) input [a,b]
fX.f'X.f''X.intX.dy.gsp
0 - toc - dx, graphing; derivitive.htm; Reimann.gsp & notes; intro 2 anti, calculators;
1 - limit by approach
2 - limit as h goes
3 - emoju&f' by m of tan line
4 - trig derivatives trick
5 - partition & sums 4 boxes
6 - Reimann & sums
7 - n=8 RLM
8 - sums f(x) - g(x)
9 - cummulative prob distr
10 - HISTORY sum to integral
11 - INTEGRATION only 1st + c
12 - INTEGRATION FTCI FTCII
13 - f(g) INTEGRATION
14 - EXTRA Notes on integration by dots
fX.f'X.f''X.intX.gsp
0 - toc - dx, graphing; derivitive.htm; Reimann.gsp & notes; intro 2 anti, calculators;
1 - limit by approach
2 - limit as h goes
3 - emoju&f' by m of tan line
4 - trig derivatives trick
5 - partition & sums 4 boxes
6 - Reimann & sums
7 - n=8 RLM
8 - sums f(x) - g(x)
9 - cummulative prob distr
10 - HISTORY sum to integral
11 - INTEGRATION only 1st + c
12 - INTEGRATION FTCI FTCII
14 - EXTRA Notes on integration by dots
fX.f'X.f''X.intX.dy.gsp
0 - toc - dx, graphing; derivitive.htm; Reimann.gsp & notes; intro 2 anti, calculators;
1 - limit by approach
2 - limit as h goes
3 - emoji &f' by m of tan line
4 - trig derivatives trick
5 - partition & sums 4 boxes
6 - Reimann & sums
7 - n=8 RLM
8 - sums f(x) - g(x) input [a,b]
9 - cummulative prob distr
10 - HISTORY sum to integral
11 - INTEGRATION only 1st + c
12 - INTEGRATION FTCI FTCII
13 - f(g) INTEGRATION
14 - EXTRA Notes on integration by dots
ReimannSums.gsp -- partitions, boxes, area by sum, antiderivative by dots
Reimann Boxes & Sums, and Integration Teacher's Manual contains:
0 - toc
1a - background limit by approach
1b - LIMIT by definition, secant
1c - partition
1d - 1st page notes
1e - 2nd page notes
2 - PARTITION & SUMS 4 boxes
3a - REIMANN & SUMS
3b - subscript x1 start
4 - n=8 RLM
5 - Hump areas
6 - area f(x)- g(x), input [a,b] in the boxes for a and b
6b - probability distribution
7 - sum to integral
8 - INTEGRATION only 1st plus c
8a - building the points (xi, sumi)
8b - Notes green dots integration
absement.gsp -- the nth derivatives of displacement
"Absement and 'nth Derivatives of Displacement' Presented Dynamically & Analytically" at MATYCNJ- MAA-NJ Joint Meeting, Kean University contains:
0 - toc
0 - 1 - time, t
0 - 2 - displacement, distance, s(t)
0 - 3 - definition of derivative
0 - 4 - s(t), s'(t)
0 - 5 - s(t), s'(t), s''(t)
0 - 6 - emojis, f, f', f'', tangent line
0 - 7 - trace derivatives
0 - 8 - PARTITION & SUMS 4 boxes
0 - 9 - Reimann & Sums
0 - 10 - SUMS absement, input [a,b]
0 - 11 - absement, n=32
0 - 12 - absement plus c
0 - 13 - play absement plus c
0 - 14 -arcsine actual fx graphed
0 - 15 - arcsine mesh - useF(x) plot to plot arcsine
JUSTdots.gsp -- Plots points on an antiderivative, no support pages
Justderivatives.gsp -- derivatives by definition, by tangent line, by traces of f', f'', f''', f''' (ideal for the trig cycle and for y=e^x)
JUSTdotsWreview.gsp -- Plots points on an antiderivative, includes some support pages

Listed by Focus - INCOMPLETE LIST

starPix -- one clean picture with just 5-pointed stars
STARS -- 4-, 5-, 6-pointed stars with instructions
complsuppl -- just complementary & supplementary angles
transversal -- corresponding, alternate interior, vertical angles and a transversal
circleFormula -- writes the formula for the depicted circle
circleTangent -- writes the tangent to a given circle
distance -- start w/a segment, coordinatize it, build triangle, use Pythagorean Theorem to find distance
polyLengthArea -- polygon pictures, notes on area and length measurement
table -- build and edit a table of data
trace -- creates point defined by an x-intercept and a calculated value for y of point
then traces the path of the point controlled by the x-intercept

2graphs.gsp -- 1,2 graphed functions, piece-wise, composite ready to edit
absValu.gsp -- 2 absolute value functions controlled by parameters
sqrt -- 2 square root functions defined by easy-edit parameters
line -- slide points A and B and generate equation of the line in 4 forms.
[[x]].gsp -- greatest integer function, also a[[bx+c]] + k
piecewise -- graphs a piecewise defined function when left function and right function and the x-value for the boundary are edited -- endpoints are not shown.
parentFX -- function "manipulatives" -- curve shift to graph functions, many functions provided
parentFX2 -- revised function "manipulatives"
generator -- used to make the parent function sketch pad
compositeFX.gsp -- build 2 functions using other functions
inverse.gsp -- take an inverse of an invertable fdunction, horizontal & vertical line tests
GraphGivenCircle -- Graph a circle by graphing + and - functions defined by parameters.
* Also states equation of circle.

parabola -- Multi page: 2 parabolas: 1 in general form, 1 in standard forms,
* both generated by equations defined by parameters.
* WITH SHOW/HIDE ACTION BUTTON
* graphs of 2 parabolas: 1 in general form, 1 in standard forms,
* 1 parabola, set a, then generat parabola w/2 points.
* 1 parabola controlled by 3 points, used for determinant analysis
* 1 vertical axis of symmetry, 1 horizontal "axis of symmetry
TracePoly -- drag point f(x) to state and show new ( x, f(x))
recipfx -- graph of parameter-defined reciprocal function,
* with slide-able tangent line,
* VERTICAL ASYMPTOTE MUST BE POSITIONED BY USER!

logs logs.gsp -- 1 - ln(x), e^x, y=x for inverse, 2 - 2 graphs, 3 - a(base)^(bx-c)+d, 4 -e by area under 1/x
Dere2x -- Derivative of the exponential
Derlnx -- Derivative of the Natural Log
e2xSums -- The Antiderivative of e^x

cosplay -- just right triangle cosine

TraceSin

sinplay -- just right triangle sine
tanplay -- just right triangle cosine

unitfx -- 6 functions with a unit circle
unitSinCosTriangle -- sine & cosine functions with a unit circle
unitTanSec -- tangent & secant functions with a unit circle
unitCotCsc -- cotangent & cosecant functions with a unit circle
Pythagorean -- using only figure to adjust angle
PythagorIdentities -- using either figure or parameter theta to adjust angle

2TrigGraphs.gsp -- 1 blank function, 1 parameter-driven function on a "trig plane"
sinplay -- just right triangle sine
cosplay -- just right triangle cosine
tanplay -- just right triangle tangent
TraceSin -- drag point f(x) to state and show new ( x, f(x))
TraceCos -- drag point f(x) to state and show new ( x, f(x))
TraceTan -- just graph with a slideable point to display coordinates
SinCosTan1stDay -- Just sine, cosine, tangent of right triangle angles.
SinCosTan6fx -- All 6 functions in right triangle only.
SinCosTanAllNumbers -- All 6 functions in right triangle and forall numbers,
* controlled by figure for right triangle,
* parameter-defined angle measure in degrees for all measures, and
* parameter-defined angle measure in decimal number times pi for radian measures
sinNcos.gsp -- sine and cosine in right triangle only
2 Sine Functions -- Asin(Bx-C) + D on 2 functions for comparison also h(x) = sine + cosine
SinTraceDerSums -- Sine from many views, right triangle, ABCD, derivative, antiderivative
polar.gsp -- r()=asin(b -c)+d

limit -- take a limit by dragging x -- drag x and see where f(x) is going or by epsilon-delta

derivativeTests -- Derivative Tests & DerAnyFx
DerAnyFx -- Derivative of Any Function
DerCos -- Derivative of Cosine
Dere2x -- Derivative of the exponential
Derlnx -- Derivative of the Natural Log
DerReciprocal -- Derivative of the Reciprocal Function
DerSqrt -- Derivative of the Square Root
limh4Dx -- Really shows the derivative is the limit of the direrence quotient. Use this one!!
DerReciprocal -- by use of a tangent line
DerAnyFx -- a function is graphed w/tangent line.
* One may trace the function and see coordinates displayed.
* One may edit the function.
* One may graph the approximate derivative function.
DERe2x -- by use of a tangent line
DerSqrt -- simple curve and tangent. Could make it fancy.
DerSquare -- simple graph w/tangent of x². Could make it fancy.

DerCos -- cosine graph, movable tangent line w/equation,
* m derived by simple m formula (h=.01),
* "derivative" may be graphed.
DerivCos -- display cosine graph and entire difference quotient triangle (not the best)
DerivSin -- full blown 4-page sketches ** Use this
DerSin -- simple sine and tangent line. Use other DerivSin.
DerTan -- tangent function & tangent line graphed, actual derivative function is provided & may be graphed.

ReimannSums.gsp -- n=8 and 32 LEFT, RIGHT, MIDPOINT slide [a,b] and set [a,b]
ReimannSumNotes.pdf -- for taking notes in class and 4 questions (graphics included)
ReimannSumANSWERS.pdf -- answers only to student notes/questions
e2xSums -- The Antiderivative of e^x

Listed Alphabetically - INCOMPLETE LIST

2graphs.gsp -- 2 graphed functions ready to edit
2parabolas.gsp -- one in standard form, one in general form
2 Sine Functions -- Asin(Bx-C) + D on 2 functions for comparison also h(x) = sine + cosine
2TrigGraphs.gsp -- 1 blank function, 1 parameter-driven function on a "trig plane"
absValu.gsp -- 2 absolute value functions controlled by parameters
circleFormula -- writes the formula for the depicted circle
circleTangent -- writes the tangent to a given circle
complsuppl -- just complementary & supplementary angles
compositeFX.gsp -- build 2 functions using other functions
conics -- circle, ellipse, hyperbola, eccentricity, parabola, family of parabolas, animation of "a," the parabola dilator
cosplay -- just right triangle cosine
DerAnyFx -- Derivative of Any Function
DerCos -- Derivative of Cosine
Dere2x -- Derivative of the exponential
derivativeTests -- Derivative Tests & DerAnyFx
Derlnx -- Derivative of the Natural Log
DerReciprocal -- Derivative of the Reciprocal Function
DerSin -- Derivative of the Sine
DerSqrt -- Derivative of the Square Root
DerSquare -- Derivative of the Square
DerTan -- Derivative of the Tangent
DerAnyFx -- a function is graphed w/tangent line.
* One may trace the function and see coordinates displayed.
* One may edit the function.
* One may graph the approximate derivative function.
DerCos -- cosine graph, movable tangent line w/equation,
* m derived by simple m formula (h=.01),
* "derivative" may be graphed.
DERe2x -- by use of a tangent line
DerivCos -- display cosine graph and entire difference quotient triangle (not the best)
DerivSin -- full blown 4-page sketches ** Use this
DERlnx -- by use of a tangent line
DerReciprocal -- by use of a tangent line
DerSin -- simple sine and tangent line. Use other DerivSin.
DerSqrt -- simple curve and tangent. Could make it fancy.
DerSquare -- simple graph w/tangent of x². Could make it fancy.
DerTan -- tangent function & tangent line graphed, actual derivative function is provided & may be graphed.
distance -- start w/a segment, coordinatize it, build triangle, use Pythagorean Theorem to find distance
e2xSums -- The Antiderivative of e^x
elevation -- angles of elevation and depression and geometry on angle created by transversal
generator -- used to make the parent function sketch pad
GraphGivenCircle -- Graph a circle by graphing + and - functions defined by parameters.
* Also states equation of circle.
[[x]].gsp -- greatest integer function, also a[[bx+c]] + k
inverse.gsp -- take an inverse of an invertable fdunction, horizontal & vertical line tests
limit -- take a limit by dragging x -- drag x and see where f(x) is going or by epsilon-delta
limh4Dx -- Really shows the derivative is the limit of the direrence quotient. Use this one!!
line -- slide points A and B and generate equation of the line in 4 forms.
logs -- 1 - ln(x), e^x, y=x for inverse, 2 - 2 graphs, 3 - a(base)^(bx-c)+d, 4 -e by area under 1/x
parabola -- Multi page: 2 parabolas: 1 in general form, 1 in standard forms,
* both generated by equations defined by parameters.
* WITH SHOW/HIDE ACTION BUTTON
* graphs of 2 parabolas: 1 in general form, 1 in standard forms,
* 1 parabola, set a, then generat parabola w/2 points.
* 1 parabola controlled by 3 points, used for determinant analysis
* 1 vertical axis of symmetry, 1 horizontal "axis of symmetry
parentFX -- function "manipulatives" -- curve shift to graph functions, many functions provided
parentFX2 -- revised function "manipulatives"
piecewise -- graphs a piecewise defined function when left function and right function and the x-value for the boundary are edited -- endpoints are not shown.
polar.gsp -- r()=asin(b -c)+d
polyLengthArea -- polygon pictures, notes on area and length measurement
Pythagorean -- using only figure to adjust angle
PythagorIdentities -- using either figure or parameter theta to adjust angle
radianSector -- arc length, sector area, radians
recipfx -- graph of parameter-defined reciprocal function,
* with slide-able tangent line,
* VERTICAL ASYMPTOTE MUST BE POSITIONED BY USER!
ReimannSumANSWERS.pdf -- answers only to student notes/questions
ReimannSumNotes.pdf -- for taking notes in class and 4 questions (graphics included)
ReimannSums.gsp -- n=8 and 32 LEFT, RIGHT, MIDPOINT slide [a,b] and set [a,b]
SinCosTan1stDay -- Just sine, cosine, tangent of right triangle angles.
SinCosTan6fx -- All 6 functions in right triangle only.
SinCosTanAllNumbers -- All 6 functions in right triangle and forall numbers,
* controlled by figure for right triangle,
* parameter-defined angle measure in degrees for all measures, and
* parameter-defined angle measure in decimal number times pi for radian measures
sinNcos.gsp -- sine and cosine in right triangle only
sinplay -- just right triangle sine
SinTraceDerSum -- Sine from many views
sqrt -- 2 square root functions defined by easy-edit parameters
starPix -- one clean picture with just 5-pointed stars
STARS -- 4-, 5-, 6-pointed stars with instructions
table -- build and edit a table of data
tanplay -- -- just right triangle tangent
trace -- creates point defined by an x-intercept and a calculated value for y of point
then traces the path of the point controlled by the x-intercept
TraceCos -- drag point f(x) to state and show new ( x, f(x))
TracePoly -- drag point f(x) to state and show new ( x, f(x))
TraceSin -- just graph with a slideable point to display coordinates
transversal -- corresponding, alternate interior, vertical angles and a transversal
unitCotCsc -- Unit circle, cosine, cosecant only
unitTanSec -- Unit circle, tangent, secant only
unitSinCosTriangle-- Unit circle, sine, cosine only
unitfx -- 6 functions with a unit circle

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