DuckieDai Arc and Sector Python Program

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geometry · MIT License

Overview

Solve arc length, sector area, radius, or angle from the radian forms of the arc and sector formulas.

Usage

Inputs

Requested unknown and known radius, arc length, sector area, or angle
Angle values are radians

Outputs

Requested arc or sector quantity with formula and units

Units: Radius and arc length use one length unit; sector area uses that unit squared; angles use radians.

Assumptions and limitations

Assumptions

The angle is measured in radians.

Constraints

Radius and divisor angles must be positive; arc length and sector area may be zero.

Known failures

Entering degrees instead of radians produces an incorrect result.

Compatibility and review

Review status: Tested on a TI calculator
Tested on: TI-84 Plus CE Python; OS 5.8.3; Python App 5.8.3.0048; exact source owner-tested through TI Connect CE
What happened: Owner confirmed the supplied arc and sector program runs on the physical calculator.
Dependencies: math
Suggested calculator name: ARCSECTR — you can give it another valid, unique name when you transfer it
Desktop test cases: Not available for this interactive-only source

This exact source auto-launches an interactive calculator session, so compatibility evidence comes from the recorded physical-device review rather than an importable desktop fixture.

Browser preview

Try arc and sector values

This browser preview calculates arc length and sector area from radius and radians. The TI program also solves the inverse modes.

Simulation boundary: This preview uses a reviewed browser adapter. It does not execute the downloaded Python and does not prove TI-Python or calculator compatibility.

JavaScript is required for the optional browser simulation. Source viewing and downloading remain available without it.

Exact reviewed bytes

Source code

Download .py

View source below, copy it when JavaScript is available, or download the exact .py bytes.

"""DuckieDai Arc & Sector for TI-84 Plus CE Python."""

from math import sqrt


def duckiedai_intro(program_name, wait=True):
    """Show the reusable DuckieDai program opening."""
    title = program_name[:16]
    empty = 16 - len(title)
    left = empty // 2
    right = empty - left

    print("+----------------------+")
    print("|   " + " " * left + title + " " * right + "   |")
    print("|                      |")
    print("|       __             |")
    print("|   ___(o )>  quack!   |")
    print("|   \\ <_. )           |")
    print("|    `---'             |")
    print("|     by DuckieDai     |")
    print("+----------------------+")
    print("Loading...")

    if wait:
        input("Press enter to start ")
        print("\n" * 6)


def positive_number(prompt):
    """Require a positive finite number."""
    while True:
        try:
            value = float(input(prompt))

            if value > 0 and value < 1e100:
                return value

        except ValueError:
            pass

        print("Enter a number above 0.")


def nonnegative_number(prompt):
    """Allow zero or positive finite numbers."""
    while True:
        try:
            value = float(input(prompt))

            if value >= 0 and value < 1e100:
                return value

        except ValueError:
            pass

        print("Enter 0 or greater.")


def show_answer(name, value, unit):
    print()
    print("ANSWER")
    print(name + " = " + str(value))
    print(unit)


def main():
    duckiedai_intro("ARC & SECTOR")

    print("ARC & SECTOR")
    print()
    print("s = r*theta")
    print("A = 0.5*r^2*theta")
    print()
    print("IMPORTANT:")
    print("theta is RADIANS")
    print()
    print("What do you need?")
    print()
    print("1. Arc length")
    print("2. Sector area")
    print("3. Radius from arc")
    print("4. Radius from area")
    print("5. Angle from arc")
    print("6. Angle from area")
    print()

    choice = input("Choose 1-6: ")

    print()

    # ==========================================
    # 1. ARC LENGTH
    #
    # s = r*theta
    # ==========================================

    if choice == "1":

        radius = positive_number(
            "Radius: "
        )

        theta = nonnegative_number(
            "Angle (radians): "
        )

        arc = radius * theta

        print()
        print("Using:")
        print("s = r*theta")
        print()
        print("s = " + str(radius))
        print("x " + str(theta))

        show_answer(
            "s",
            arc,
            "units"
        )

    # ==========================================
    # 2. SECTOR AREA
    #
    # A = 0.5*r^2*theta
    # ==========================================

    elif choice == "2":

        radius = positive_number(
            "Radius: "
        )

        theta = nonnegative_number(
            "Angle (radians): "
        )

        area = (
            0.5 *
            radius ** 2 *
            theta
        )

        print()
        print("Using:")
        print("A = 0.5*r^2*theta")
        print()
        print("A = 0.5 x")
        print(str(radius) + "^2")
        print("x " + str(theta))

        show_answer(
            "A",
            area,
            "square units"
        )

    # ==========================================
    # 3. RADIUS FROM ARC LENGTH
    #
    # r = s/theta
    # ==========================================

    elif choice == "3":

        arc = nonnegative_number(
            "Arc length: "
        )

        theta = positive_number(
            "Angle (radians): "
        )

        radius = arc / theta

        print()
        print("Using:")
        print("s = r*theta")
        print()
        print("Rearranged:")
        print("r = s/theta")

        show_answer(
            "r",
            radius,
            "units"
        )

    # ==========================================
    # 4. RADIUS FROM SECTOR AREA
    #
    # r = sqrt(2A/theta)
    # ==========================================

    elif choice == "4":

        area = nonnegative_number(
            "Sector area: "
        )

        theta = positive_number(
            "Angle (radians): "
        )

        radius = sqrt(
            (2 * area) /
            theta
        )

        print()
        print("Using:")
        print("A = 0.5*r^2*theta")
        print()
        print("Rearranged:")
        print("r = sqrt(2A/theta)")

        show_answer(
            "r",
            radius,
            "units"
        )

    # ==========================================
    # 5. ANGLE FROM ARC LENGTH
    #
    # theta = s/r
    # ==========================================

    elif choice == "5":

        arc = nonnegative_number(
            "Arc length: "
        )

        radius = positive_number(
            "Radius: "
        )

        theta = arc / radius

        print()
        print("Using:")
        print("s = r*theta")
        print()
        print("Rearranged:")
        print("theta = s/r")

        show_answer(
            "theta",
            theta,
            "radians"
        )

    # ==========================================
    # 6. ANGLE FROM SECTOR AREA
    #
    # theta = 2A/r^2
    # ==========================================

    elif choice == "6":

        area = nonnegative_number(
            "Sector area: "
        )

        radius = positive_number(
            "Radius: "
        )

        theta = (
            2 * area /
            (radius ** 2)
        )

        print()
        print("Using:")
        print("A = 0.5*r^2*theta")
        print()
        print("Rearranged:")
        print("theta = 2A/r^2")

        show_answer(
            "theta",
            theta,
            "radians"
        )

    else:
        print("Invalid choice.")

    print()
    print("DuckieDai says: done!")


# TI-Python imports the selected AppVar rather than
# setting __name__ to main.
main()

"""DuckieDai Arc & Sector for TI-84 Plus CE Python."""
from math import sqrt
def duckiedai_intro(program_name, wait=True):
"""Show the reusable DuckieDai program opening."""
title = program_name[:16]
empty = 16 - len(title)
left = empty // 2
right = empty - left
print("+----------------------+")
print("| " + " " * left + title + " " * right + " |")
print("| |")
print("| __ |")
print("| ___(o )> quack! |")
print("| \\ <_. ) |")
print("| `---' |")
print("| by DuckieDai |")
print("+----------------------+")
print("Loading...")
if wait:
input("Press enter to start ")
print("\n" * 6)
def positive_number(prompt):
"""Require a positive finite number."""
while True:
try:
value = float(input(prompt))
if value > 0 and value < 1e100:
return value
except ValueError:
pass
print("Enter a number above 0.")
def nonnegative_number(prompt):
"""Allow zero or positive finite numbers."""
while True:
try:
value = float(input(prompt))
if value >= 0 and value < 1e100:
return value
except ValueError:
pass
print("Enter 0 or greater.")
def show_answer(name, value, unit):
print()
print("ANSWER")
print(name + " = " + str(value))
print(unit)
def main():
duckiedai_intro("ARC & SECTOR")
print("ARC & SECTOR")
print()
print("s = r*theta")
print("A = 0.5*r^2*theta")
print()
print("IMPORTANT:")
print("theta is RADIANS")
print()
print("What do you need?")
print()
print("1. Arc length")
print("2. Sector area")
print("3. Radius from arc")
print("4. Radius from area")
print("5. Angle from arc")
print("6. Angle from area")
print()
choice = input("Choose 1-6: ")
print()
# ==========================================
# 1. ARC LENGTH
#
# s = r*theta
# ==========================================
if choice == "1":
radius = positive_number(
"Radius: "
)
theta = nonnegative_number(
"Angle (radians): "
)
arc = radius * theta
print()
print("Using:")
print("s = r*theta")
print()
print("s = " + str(radius))
print("x " + str(theta))
show_answer(
"s",
arc,
"units"
)
# ==========================================
# 2. SECTOR AREA
#
# A = 0.5*r^2*theta
# ==========================================
elif choice == "2":
radius = positive_number(
"Radius: "
)
theta = nonnegative_number(
"Angle (radians): "
)
area = (
0.5 *
radius ** 2 *
theta
)
print()
print("Using:")
print("A = 0.5*r^2*theta")
print()
print("A = 0.5 x")
print(str(radius) + "^2")
print("x " + str(theta))
show_answer(
"A",
area,
"square units"
)
# ==========================================
# 3. RADIUS FROM ARC LENGTH
#
# r = s/theta
# ==========================================
elif choice == "3":
arc = nonnegative_number(
"Arc length: "
)
theta = positive_number(
"Angle (radians): "
)
radius = arc / theta
print()
print("Using:")
print("s = r*theta")
print()
print("Rearranged:")
print("r = s/theta")
show_answer(
"r",
radius,
"units"
)
# ==========================================
# 4. RADIUS FROM SECTOR AREA
#
# r = sqrt(2A/theta)
# ==========================================
elif choice == "4":
area = nonnegative_number(
"Sector area: "
)
theta = positive_number(
"Angle (radians): "
)
radius = sqrt(
(2 * area) /
theta
)
print()
print("Using:")
print("A = 0.5*r^2*theta")
print()
print("Rearranged:")
print("r = sqrt(2A/theta)")
show_answer(
"r",
radius,
"units"
)
# ==========================================
# 5. ANGLE FROM ARC LENGTH
#
# theta = s/r
# ==========================================
elif choice == "5":
arc = nonnegative_number(
"Arc length: "
)
radius = positive_number(
"Radius: "
)
theta = arc / radius
print()
print("Using:")
print("s = r*theta")
print()
print("Rearranged:")
print("theta = s/r")
show_answer(
"theta",
theta,
"radians"
)
# ==========================================
# 6. ANGLE FROM SECTOR AREA
#
# theta = 2A/r^2
# ==========================================
elif choice == "6":
area = nonnegative_number(
"Sector area: "
)
radius = positive_number(
"Radius: "
)
theta = (
2 * area /
(radius ** 2)
)
print()
print("Using:")
print("A = 0.5*r^2*theta")
print()
print("Rearranged:")
print("theta = 2A/r^2")
show_answer(
"theta",
theta,
"radians"
)
else:
print("Invalid choice.")
print()
print("DuckieDai says: done!")
# TI-Python imports the selected AppVar rather than
# setting __name__ to main.
main()

Filename: ARCSECTR.py
Size: 6247 bytes
SHA-256: 5f9e97ec66f6e40785ab7d95e731ccf20532171354adb2dd98ca18a156ade831

Transfer and launch

Confirm that your calculator is the Python-capable model named above. Check that its OS and Python App versions match the reviewed record.
Download the .py source above and verify its SHA-256 digest if your computer provides that option.
Use TI Connect CE to send the Python file to a compatible calculator. ARCSECTR is a suggested name; you may choose another valid, unique calculator name.
Open the Python App, select the program, and check sample inputs before relying on other results.

Read the complete installation, launch, troubleshooting, and removal guide.

Availability does not mean a teacher, school, or exam permits this program. Follow the applicable rules.

Version history

1.0.0 — current version, published 2026-09-24. Download this reviewed version

Any source change requires a new immutable version and digest. Historical downloads remain available only while their review records remain valid.

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