It’s a pretty easy concept to find the length of a straight line. Take out a ruler or tape measure and find the length. Even on a map or graph, finding the distance from point A to point B is quickly accomplished.
Making the leap to a curving line or squiggly course on a map is a totally different experience. Now you’ve introduced the challenge of applying geometric principles and even the use of calculus.
What makes the task easier? Putting geometric principles into action with a calculator capable of solving the arc length of a curve.
What is an Arc Length?
You’re no-doubt familiar with the form of a circle, including that the concept that the length of the circumference can be calculated by using the formula C = 2 r, where r = the radius of the circle. But taking only a segment of the circle’s circumference, how do you measure the length of that arc of the circle?
Arc length calculators apply calculus in solving the equation.
Why You Need to Know Arc Length
Think about it – there are many applications where calculating an arc length may be invaluable:
- Building highways – engineers need to accurately calculate each curve to ensure vehicles can traverse them safely at their rated speed
- Plotting courses for aviators or marine travel. The Earth is a circle, making the curvature (yes, an arc) an important factor when planning for travel time – and fuel required for the trip
- Cutting your pizza – just to make sure your slice has as large an arc as everyone else’s
- When manufacturing products that include a curvature, companies must calculate the arc to plan material requirements accurately
All these examples just scratch the surface of why an accurate length of an arc calculator can be an important tool.
Try it Yourself
Calculating the arc length of a circle segment is reasonably straight-forward:
- If you have a sketch or circular item, you can measure the radius and use the formula above to solve the circumference.
- Armed with that value, you can pull out the old protractor to measure the angle of the sector you want to measure for the arc.
- Your angle is the numerator of a fraction, with 360 (degrees in the entire circle) being the denominator.
- Divide the numerator by the denominator to arrive at a decimal value, then multiplying that value by the circumference, and you have your arc length.
Easy, right? Maybe not for everyone, and certainly prone to errors at any step along the way. Of course, the other caveat is that you must have the circular item or sketch readily available for this method, and you need a protractor at your disposal.
Why Not Use a Calculator?
Tools were made to be used and calculating arc length or anything that utilizes calculus certainly warrants the application of a scientific/graphing calculator to do the job.
Calculating the arc length of a circle segment is a simple job for a graphing calculator. Functions available on most scientific calculators will make quick work of arc length calculations, with much less potential for error.
Learning to Apply Geometry Calculator Functions
There are several ways to gain skills in using scientific calculators to solve geometric problems.
Manufacturers such as Texas Instruments provide training for educators that help in developing curriculums focused on mathematical skills, including working with geometry calculators to solve problems and understand such functions as:
- Circle and triangle relationships
- Volume formulas and how to use them
- Theorems related to circles, including finding arclength calculations and sector areas
Other resources also make the task easier:
Need a problem solved, but don’t have a scientific calculator handy? There are plenty of online arc length calculators available for your use. Many offer geometry calculator functions:
- Central angle
- Sector area
- Arc length
As handy and cost-effective as online tools are, nothing beats the transportability and availability of a palm-sized calculator designed especially for these purposes.
What a great segue into another resource – the device that may be in the palm of your hand as you read this.
Your smartphone or tablet.
Making Your Choice
Many consumers enjoy the convenience of having scientific calculator functions included right on their smartphones. For others, an online calculator serves their purposes just fine.
For those who will be using calculus functions on a regular basis to determine the arc length of a curve or other purposes, a full-function graphing or scientific calculator will prove to be a good investment.
Feature image via 1728