Initial commit

.gitattributes

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+# Auto detect text files and perform LF normalization
+* text=auto

LICENSE.md

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+Copyright (c) 2020 Joan Horvath and Rich Cameron
+
+These models are licensed under a [Creative Commons Attribution 4.0 International license](https://creativecommons.org/licenses/by/4.0/).

README.md

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+# Calculus
+
+This repository contains 3D printable calculus models for our book, [Make: Calculus](https://www.amazon.com/dp/168045739X/).
+
+This project was supported, in part by grant number 90RE5024, from the U.S. Administration for Community Living, Department of Health and Human Services, Washington, D.C. 20201.
+
+License [CC-BY-4.0](https://creativecommons.org/licenses/by/4.0/), with attribution: “Joan Horvath and Rich Cameron (with link to this repository).”

arduino_demos/integral_mouse.ino

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+// File led_pendulum.ino
+// Makes a Circuit Playground or Circuit Playground Express
+// light up with one of three colors, depending on the acceleration
+// seen on a chosen axis
+// (c) 2022 Rich Cameron, for the book Make:Calculus
+// Licensed under a Creative Commons, Attribution,
+// CC-BY 4.0 international license, per
+// https://creativecommons.org/licenses/by/4.0/
+// Attribute to Rich Cameron, at
+// repository github.com/whosawhatsis/Calculus
+
+#include <Adafruit_CircuitPlayground.h>
+
+#define X //capital X, Y or Z, the direction you will be swinging
+//use Y for Classic, X for Express (with USB pointed up)
+//(see the markings by your board's accelerometer)
+#define THRESHOLD 0.3
+
+void setup() {
+  CircuitPlayground.begin();
+  CircuitPlayground.setBrightness(255);
+  CircuitPlayground.clearPixels();
+}
+
+void loop() {
+  float motion =
+    #if defined(X)
+      CircuitPlayground.motionX();
+    #elif defined(Y)
+      -CircuitPlayground.motionY();
+    #elif defined(Z)
+      CircuitPlayground.motionZ();
+    #else
+      #error No valid axis specified.
+    #endif
+
+  CircuitPlayground.clearPixels();
+  if(motion > THRESHOLD) for(int i = 0; i < 3; i++)
+    CircuitPlayground.setPixelColor(i, 255, 0, 0);
+  else if(motion < -THRESHOLD) for(int i = 7; i < 10; i++)
+    CircuitPlayground.setPixelColor(i, 0, 0, 255);
+  else for(int i = 4; i < 6; i++)
+  CircuitPlayground.setPixelColor(i, 0, 255, 0);
+}

arduino_demos/led_pendulum.ino

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+// File led_pendulum.ino
+// Makes a Circuit Playground or Circuit Playground Express
+// light up with one of two colors, depending on the acceleration
+// seen on a chosen axis
+// (c) 2022 Rich Cameron, for the book Make:Calculus
+// Licensed under a Creative Commons, Attribution,
+// CC-BY 4.0 international license, per
+// https://creativecommons.org/licenses/by/4.0/
+// Attribute to Rich Cameron, at
+// repository github.com/whosawhatsis/Calculus
+
+#include <Adafruit_CircuitPlayground.h>
+
+#define Y //capital X, Y or Z, this is the direction you will be swinging (see the markings by your board's accelerometer).
+#define THRESHOLD 0.3
+
+void setup() {
+  CircuitPlayground.begin();
+  CircuitPlayground.setBrightness(255);
+  CircuitPlayground.clearPixels();
+}
+
+void loop() {
+  float motion =
+    #if defined(X)
+      CircuitPlayground.motionX();
+    #elif defined(Y)
+      -CircuitPlayground.motionY();
+    #elif defined(Z)
+      CircuitPlayground.motionZ();
+    #else
+      #error No valid axis specified.
+    #endif
+
+  CircuitPlayground.clearPixels();
+  if(motion > THRESHOLD) for(int i = 0; i < 3; i++)
+    CircuitPlayground.setPixelColor(i, 255, 0, 0);
+  else if(motion < -THRESHOLD) for(int i = 7; i < 10; i++)
+    CircuitPlayground.setPixelColor(i, 0, 0, 255);
+  else for(int i = 4; i < 6; i++)
+  CircuitPlayground.setPixelColor(i, 0, 255, 0);
+}

cones/coneOfCylinders.scad

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+// File coneOfCylinders.scad
+// Creates a cone (or pyramid) of stacked cylinders
+// based on volume and height of the approximated cone
+// (actual volume will be greater)
+// (c) 2019-2022 Rich Cameron, for the book Make:Calculus
+// Licensed under a Creative Commons, Attribution,
+// CC-BY 4.0 international license, per
+// https://creativecommons.org/licenses/by/4.0/
+// Attribute to Rich Cameron, at
+// repository github.com/whosawhatsis/Calculus
+
+cylinders = 3;
+offset = [0, 0];
+
+v = 50000; // volume in cubic mm (cc * 1000)
+h = 90; // height in mm
+n = 300; // number of sides (not including bottom)
+
+// STL files don't have curves, so a cone must be approximated by using a large number for n. Depending on size, you'll want to find a value for area that results in a side length (check the console output) around 0.2-0.5mm. Sides shorter than this will not look smoother noticeably smoother once printed.
+
+// the rest is calculated...
+
+a = v / h * 3; // base-sectional area
+s = 2 * sqrt(a * tan(180 / n) / n);
+apothem = (2 * a / n / s);
+r = apothem / cos(180 / n);
+
+for(i = [0:cylinders - 1]) translate([offset[0] * (1 - i / cylinders), offset[1] * (1 - i / cylinders), i * h / cylinders]) cylinder(r = r * (cylinders - i) / cylinders, h = h / cylinders, $fn = n);
+
+	echo(str("base-sectional area: ", a)); // base-sectional area
+	echo(str("side: ", s)); // side
+	echo(str("radius: ", r)); // radius
+	if((n % 2)) echo(str("radius + apothem: ", r + apothem)); // radius + apothem (only calculated for an odd number of sides)
+	echo(str("apothem: ", apothem)); // apothem
+	echo(str("circumscribed circle area: ", PI * pow(r, 2))); // circumscribed circle area
+	echo(str("inscribed circle area: ", PI * pow(apothem, 2))); // inscribed circle area
+	echo(str("polygon area: ", .5 * n * s * r * cos(180 / n))); // polygon area

cones/obliqueCone.scad

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+// File obliqueCone.scad
+// Creates a hollow oblique cone (or pyramid) based on 
+// volume and height
+// (c) 2016-2022 Rich Cameron, for the book Make:Calculus
+// Licensed under a Creative Commons, Attribution,
+// CC-BY 4.0 international license, per
+// https://creativecommons.org/licenses/by/4.0/
+// Attribute to Rich Cameron, at
+// repository github.com/whosawhatsis/Calculus
+
+// enter these three variables:
+
+v = 50000; // volume in cubic mm (cc * 1000)
+h = 90; // height in mm
+n = 300; // number of sides (not including bottom)
+
+wall = 1;
+tol = .2;
+lid = true;
+lip = .25;
+ball = 0;
+offset = [30, 0];
+
+// STL files don't have curves, so a cone must be approximated by using a large number for n. Depending on size, you'll want to find a value for area that results in a side length (check the console output) around 0.2-0.5mm. Sides shorter than this will not look smoother noticeably smoother once printed.
+
+// the rest is calculated...
+
+a = v / h * 3; // base-sectional area
+s = 2 * sqrt(a * tan(180 / n) / n);
+apothem = (2 * a / n / s);
+r = apothem / cos(180 / n);
+
+difference() {
+	union() {
+		hull() {
+			translate([0, 0, h]) mirror([0, 0, 1]) cylinder(r = 0 + wall, $fn = n, h = .0001);
+			translate(offset) cylinder(r = r + wall, $fn = n, h = .0001);
+		}
+		if(ball) translate([0, 0, h - ball / 2 * cos(asin(2 * wall / ball))]) intersection() {
+			sphere(ball / 2, $fs = .2, $fa = 2);
+		}
+	}
+	difference() {
+		linear_extrude(h * 2, scale = 0, center = true) translate(offset * 2) circle(r * 2, $fn = n);
+		linear_extrude(1, center = true) translate(offset) difference() {
+			circle(r * 2, $fn = n);
+			circle(r - wall, $fn = n);
+		}
+	}
+}
+
+echo(str("base-sectional area: ", a)); // base-sectional area
+echo(str("side: ", s)); // side
+echo(str("radius: ", r)); // radius
+if((n % 2)) echo(str("radius + apothem: ", r + apothem)); // radius + apothem (only calculated for an odd number of sides)
+echo(str("apothem: ", apothem)); // apothem
+echo(str("circumscribed circle area: ", PI * pow(r, 2))); // circumscribed circle area
+echo(str("inscribed circle area: ", PI * pow(apothem, 2))); // inscribed circle area
+echo(str("polygon area: ", .5 * n * s * r * cos(180 / n))); // polygon area

cones/simpleCone.scad

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+// File simpleCone.scad
+// Creates a cone (or pyramid) based on volume and height
+// (c) 2016-2022 Rich Cameron, for the book Make:Calculus
+// Licensed under a Creative Commons, Attribution,
+// CC-BY 4.0 international license, per
+// https://creativecommons.org/licenses/by/4.0/
+// Attribute to Rich Cameron, at
+// repository github.com/whosawhatsis/Calculus
+
+// enter these three variables:
+
+v = 50000; // volume in cubic mm (cc * 1000)
+h = 90; // height in mm
+n = 300; // number of sides (not including bottom)
+
+// STL files don't have curves, so a cone must be approximated by using a large number for n. Depending on size, you'll want to find a value for area that results in a side length (check the console output) around 0.2-0.5mm. Sides shorter than this will not look smoother noticeably smoother once printed.
+
+// the rest is calculated...
+
+a = v / h * 3; // base-sectional area
+s = 2 * sqrt(a * tan(180 / n) / n);
+apothem = (2 * a / n / s);
+r = apothem / cos(180 / n);
+
+linear_extrude(h, scale = 0) translate(offset) difference(){
+	circle(r, $fn = n);
+	//square(r);
+}
+
+	echo(str("base-sectional area: ", a)); // base-sectional area
+	echo(str("side: ", s)); // side
+	echo(str("radius: ", r)); // radius
+	if((n % 2)) echo(str("radius + apothem: ", r + apothem)); // radius + apothem (only calculated for an odd number of sides)
+	echo(str("apothem: ", apothem)); // apothem
+	echo(str("circumscribed circle area: ", PI * pow(r, 2))); // circumscribed circle area
+	echo(str("inscribed circle area: ", PI * pow(apothem, 2))); // inscribed circle area
+	echo(str("polygon area: ", .5 * n * s * r * cos(180 / n))); // polygon area

coordinate_systems/cartesianGrid.scad

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+// File cartesianGrid.scad
+// Creates a cube and segments for a cartesian coordinate system
+// (c) 2019-2022 Rich Cameron, for the book Make:Calculus
+// Licensed under a Creative Commons, Attribution,
+// CC-BY 4.0 international license, per
+// https://creativecommons.org/licenses/by/4.0/
+// Attribute to Rich Cameron, at
+// repository github.com/whosawhatsis/Calculus
+
+segments = false; // true to generate segments, false to generate grid
+
+grid = 15;//size of each cube, mm
+size = 3; // size of one-quarter of overall demonstration cube
+
+if(segments) {
+	%grid();
+	segment();
+} else {
+	grid();
+	%segment();
+}
+
+module grid() difference() {
+	linear_extrude(grid * size * 2, center = true, convexity = 5) difference() {
+		square(grid * size * 2, center = true);
+		for(i = [0, 1]) mirror([i, -i, 0]) for(i = [0, 1]) mirror([i, i, 0]) for(x = [-size:size]) translate([x * grid, grid * size, 0]) circle(1, $fn = 4);
+	}
+	for(i = [0, 1], j = [0, 1], k = [0, 1]) mirror([0, 0, k]) mirror([-k, k, 0]) mirror([i, i, 0]) mirror([j, 0, j])  mirror([0, 1, 1]) linear_extrude(grid * size * 2, center = true) for(x = [-size:size]) translate([x * grid, grid * size, 0]) circle(1, $fn = 4);
+	intersection_for(i = [0, 1]) mirror([i, i, 0]) intersection_for(i = [0, 1]) mirror([i, 0, i]) cylinder(r = 1, h = 3, $fn = 4, center = true);
+	for(i = [0, 1], j = [0, 1]) mirror([j, -j, 0]) mirror([i, 0, -i]) linear_extrude(grid * size * 2, convexity = 5) {
+		square(grid * size * 2);
+		for(i = [0, 1]) mirror([i, -i, 0]) for(x = [0:size - 1]) translate([x * grid, 0, 0]) circle(1, $fn = 4);
+	}
+}
+
+module segment() difference() {
+	linear_extrude(grid) difference() {
+		square(grid);
+		for(x = [0, 1], y = [0, 1]) translate([x * grid, y * grid, 0]) circle(1, $fn = 4);
+	}
+	for(i = [0, 1]) mirror([i, -i, 0]) for(i = [0, 1]) mirror([1, 0, -1]) linear_extrude(grid) for(x = [0, 1], y = [0, 1]) translate([x * grid, y * grid, 0]) circle(1, $fn = 4);
+}

coordinate_systems/cylinderGrid.scad

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+// File cylinderGrid.scad
+// Creates a cylinder and segments for a cylindrial coordinate system
+// (c) 2019-2022 Rich Cameron, for the book Make:Calculus
+// Licensed under a Creative Commons, Attribution,
+// CC-BY 4.0 international license, per
+// https://creativecommons.org/licenses/by/4.0/
+// Attribute to Rich Cameron, at
+// repository github.com/whosawhatsis/Calculus
+
+segments = false; // true to generate segments, false to generate grid
+
+grid = 15;
+grid_angle = 360 / 4 / 3;
+size = 3;
+
+$fs = .2;
+$fa = 2;
+
+if(segments) {
+	%grid();
+	for(i = [0:size - 1]) translate([i + 1, 1, 0]) segment(i);
+} else {
+	grid();
+	for(i = [0:size - 1]) %segment(i);
+}
+
+module grid() difference() {
+	linear_extrude(grid * size * 2, center = true, convexity = 5) difference() {
+		circle(grid * size);
+		for(a = [0:grid_angle:359]) rotate(a) translate([grid * size, 0, 0]) circle(1, $fn = 4);
+	}
+	*intersection_for(i = [0, 1]) mirror([i, i, 0]) intersection_for(i = [0, 1]) mirror([i, 0, i]) cylinder(r = 1, h = 3, $fn = 4, center = true);
+	linear_extrude(grid * size * 2, convexity = 5) {
+		square(grid * size * 2);
+		for(i = [0, 1]) mirror([i, -i, 0]) for(x = [1:size - 1]) translate([x * grid, 0, 0]) circle(1, $fn = 4);
+		circle(1);
+	}
+	hull() for(i = [0, 1]) mirror([0, 0, i]) cylinder(r = 1, r2 = 0, h = 1);
+	for(i = [-1, 1]) translate([0, 0, i * grid * size]) {
+		rotate_extrude() difference() {
+			union() for(x = [0:size - 1]) translate([x * grid, 0, 0]) circle(1, $fn = 4);
+			translate([-1, 0, 0]) square(2, center = true);
+		}
+		for(a = [0:grid_angle:179]) rotate(a) mirror([1, 0, 1]) linear_extrude(grid * size * 2, center = true, convexity = 5) circle(1, $fn = 4);
+	}
+	for(z = [-size:size]) translate([0, 0, z * grid]) rotate_extrude() translate([size * grid, 0, 0]) circle(1, $fn = 4);
+	intersection() {
+		rotate_extrude() difference() {
+			union() for(x = [0:size]) translate([x * grid, 0, 0]) circle(1, $fn = 4);
+			translate([-1, 0, 0]) square(2, center = true);
+		}
+		linear_extrude(2, center = true) square(grid * size * 2);
+	}
+	for(z = [0:size - 1]) translate([0, 0, z * grid]) for(a = [0:grid_angle:90]) rotate(a) mirror([1, 0, -1]) linear_extrude(grid * size * 2, convexity = 5) circle(1, $fn = 4);
+}
+
+module segment(choord = 0) difference() {
+	linear_extrude(grid) difference() {
+		intersection() {
+			difference() {
+				circle((choord + 1) * grid);
+				circle(choord * grid);
+			}
+			square(grid * size * 2);
+			rotate(grid_angle - 90) square(grid * size * 2);
+		}
+		for(a = [0, grid_angle]) rotate(a) for(x = [1:size]) translate([x * grid, 0, 0]) circle(1, $fn = 4);
+		circle(1);
+	}
+	for(i = [0, 1]) translate([0, 0, i * grid]) {
+		rotate_extrude() difference() {
+			for(x = [0:size]) translate([x * grid, 0, 0]) circle(1, $fn = 4);
+			translate([-1, 0, 0]) square(2, center = true);
+		}
+		for(a = [0:grid_angle:179]) rotate(a) mirror([1, 0, 1]) linear_extrude(grid * size * 2, center = true, convexity = 5) circle(1, $fn = 4);
+	}
+}