## Math, Waves, and the Creator: Light Waves

Part 2 of 3

Note: This is a continuation of a series of guest posts on Math, Waves, and the Creator by Dr. Adam F. Hannon. This particular one would be great to have middle school and high school students read in order to give them a glimpse into how math helps us shine light on God’s creation, pointing to the Creator. I hope you enjoy! – Katherine

“And God said, Let there be light: and there was light.” Genesis 1:3 (KJV)

God spoke, and light came into being. We feel its warmth (very much so in the summer months!) and enjoy its illumination, yet math gives us a fresh glimpse into just how amazing all the light around us is.

As discussed in the previous “Wave, Math, and the Creator” blog post, light is a wave—or more specifically, two coupled waves (an electric and a magnetic wave) in one. We saw in the previous blog how we can use algebra and trigonometry to describe waves, including light waves.

Let’s continue exploring light with math—only this time, we’ll use basic math, along with just a touch of algebra (the part a pre-algebra student could still follow).

As we do so, we’ll discover amazing order God placed in the very light all around us.

## Measuring the Properties of Light Waves

There are a lot of different aspects of light waves we could look at. For example, we could look at how fast a wave is traveling in a certain direction—or its velocity.

We can use a number to describe this velocity.

Figure 1.1 The velocity of a wave is how fast the wave is traveling in a certain direction. For example, if the  wave above took 1 second to travel 1 centimeter toward the right, we would say its velocity was 1 centimeter per second, or 1 cm/sec.

Or we could look at how frequently one part of the wave repeats in a given amount of time, called the frequency.

Again, we can use a number to describe the frequency.

Figure 1.2: In the video, the two waves have the same wavelength but different frequencies. During the time it takes the top green wave to pass one full period through the dashed line, the bottom purple wave passes through twice, thus it has twice the frequency.

We can also look at the wavelength—at how long each of the repeated wave structures are.

Again, we can use a number to describe the wavelength!

Figure 1.3 The marked distance between the peak of each wave is the wavelength. Notice that the top wave has a greater wavelength than the bottom one.

Now, in real life, it’s not easy to measure the frequency of a light wave—it corresponds to a really short amount of time. But it is easier to measure the wavelength. And then—you guessed it!—we can use math to help us find the frequency. Let’s take a look at how.

## Using Math to Find the Frequency

Because of the consistent way God governs all things, there is a consistent relationship between the velocity, frequency, and wavelength of a wave:

velocity = frequencywavelength

Since in math we tend to use letters instead of writing out the whole words (it saves time and makes it a lot easier to work with the equation!), we’ll use symbols to represent this same relationship (the v represents the velocity, the f the frequency, and the λ the wavelength):

v = f λ

Now that we know the relationship between the velocity, frequency, and wavelength [1], we can use math to help us figure out the frequency. In a light wave, the velocity is the speed of light, which, because of the consistent way God governs all things, is always constant 670,616,629 miles per hour (or roughly 3.00 x 1017nm/sec). Note: The “sec” stands for “second,” and the nm stands for nanometers or 1 billionth the length of a meter—it’s very small! Thus, we can write that amount for the velocity (which we represented with a v) in the equation, giving us this:

3.00 x 1017 nm/sec = f λ

And now if we know the wavelength, we can easily find the frequency!

Example: If the wavelength (λ) of a light wave is 650 nm, what is its frequency?

We know this relationship: 3.00 x 1017 nm/sec = f λ

Substituting in 650 nm for the wavelength (λ) gives us this: 3.00 x 1017 nm/sec = f(650 nm)

If we now divide both sides by 650 nm, we’ll find the frequency.

Note: Notice that we divided both sides by the same amount to simplify the answer—we’re able to do that because of the consistent way God governs creation.

The THz stands for Terahertz. Tera means a trillion. We just saw that a 650 nm light wave has a frequency of 462 Terahertz; in other words, it is repeating the wave-like pattern 462 trillion times per second! Can you imagine something happening a trillion times over and over again in a single second!?

## Discovering the Colors of Light—and Invisible Light

One of the neat things we discover as we use math to explore light is that different wavelengths result in different colors.

While we are used to white light, we also encounter colored lights, such as the red light in a small laser pointer. Notice how the color varies as the wavelength varies.

Figure 1.4: Approximate wavelengths of different colored lights.[2]

Some light, though, is invisible. It turns out that there are more to light waves than just what we think of as “light”! There are kinds of light waves with smaller and larger wavelengths that we can consider as invisible light. These different invisible light waves along with visible light are all called electromagnetic waves and make up a whole spectrum as shown in the figure below.

Figure 1.5: Schematic of the electromagnetic spectrum. Going from left to right goes from longer wavelengths to shorter wavelengths.

Just think of the fact we can also only see a small portion of the electromagnetic spectrum—what beauty must exist to God who can see in the entire spectrum!

We are literally “in the dark” to most of the light waves around us—we only know much about them because we can use tools and equipment to detect them.

## Applying What We Learn About Light

Not only does math help us appreciate the amazing beauty God put in light, but math helps us apply what we learn to build technology.

For example, take CDs, DVDs, and “Blue-Ray” discs. Did you know that the CD/DVD/Blue-Ray player reads the data off these disks using light, and that each of them use light with different wavelengths (and thus different colors)[3]?

• CDs – 780 nm wavelength (infrared)
• DVDs – 650 nm wavelength (red)
• Blue-ray – 405 nm wavelength (indigo…somebody named that wrong!)

Every time you use a CD/DVD/Blue-ray disc, you’re reaping the benefits of math in action.

## Let There Be Light

That’s just a glimpse into how math reveals design and beauty in the very light around us—the light God created by the simple command, “Let there be light” (Genesis 1:3 KJV).

As you enjoy the bright summer light today, pause and reflect on the Creator’s power and might Who simply spoke light into existence.

He is the same Creator who shone into the darkness of our sin with the Light—Jesus Christ.

“In him was life; and the life was the light of men. And the light shineth in darkness; and the darkness comprehended it not…. But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name:” John 1:3-4, 12 (KJV)

Note: Stay tuned for the final blog in the Waves, Math, and the Creator series. In it, we’ll explore sound waves.

[1] Equation from David J. Griffiths, Introduction to Electrodynamics, 3rd ed. (USA: Upper Saddle River, NJ: Prentice Hall, 1999), p. 368.
[2] The exact colors given for different lights varies by source, as the there are a range of hues within red, orange, etc., and the borders are hard to concretely define since what may be orange to one person might still be red to another (see this Live Physics page for one list of approximate ranges). The point is that different colors of light do have different wavelengths. These values came from those given in Griffiths, p. 377. The figure was adapted with those numbers from one by Gringer.
[3] Values from Kumar, T. Ravi, and R. V. Krishnaiah. “Optical Disk with Blu-Ray Technologoy.” International Journal of Computer Engineering & Applications III, no. II/III (July-September 2013), p. 160. https://arxiv.org/ftp/arxiv/papers/1310/1310.1551.pdf.

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## Now Available: Elementary and High School Math Curriculum

Looking for a math curriculum for your elementary students that is easy to use, teaches math as a real-life tool, AND encourage students spiritually through explorations of God’s creation and character-building stories? How about an algebra and geometry course that shows students why they’re learning what they’re learning?

I’m excited to announce that we’re now carrying elementary through high school math curriculum that teach math as a real-life tool. I’ve put more details about the curriculum below. And you can read more and view samples in our store. I hope they will prove helpful to you in showing your students how math isn’t meaningless—it’s a real-life tool that proclaims the Creator’s praises.

### Elementary Math Curriculum: Math Lessons for a Living Education

This is the first program I’ve found that

• presents math as a real-life tool;
• has an easy-to-use textbook approach that minimizes parental preparation and thought, AND
• encourages students spiritually through explorations of God’s creation and character-building stories.

Students will love the stories about children who discover different math concepts in real life. Rather than just being told to memorize facts, they’ll get to discover those facts along with the children and then work worksheets related to that story. The stories all come from a young-earth creationist perspective and illustrate life lessons and good character along the way. Plus, they’re full-color and beautifully illustrated!

Another thing I love about this program is that there’s only one book to buy for the program itself–you don’t need to purchase separate student and teacher’s books. All of the levels include an easy-to-use schedule at the front, along with any notes the teacher needs right there. Level 1 and 2 include a link to download the answers, while Level 3-5 include the answers in the back of the book (the pages are all perforated and hole punched, so parents/teachers can easily pull this section out and place in a binder).

While the program doesn’t necessarily talk about the philosophy of math (why it works, how its very existence points to God, etc.) or math’s history, it presents math in conjunction with God’s creation in a refreshingly simple way. Unlike with many curricula, you won’t have to rework the presentations or try to figure out how to add science or real-life examples—they’re already there, and done amazingly well. Parents could easily add little nuggets about the “why” and the history of math as they go (see Revealing Arithmetic or Beyond Numbers for ideas).

### Junior High Math Curriculum: Principles of Mathematics

This is the series I wrote to both firm up elementary math and give students a big picture understanding of high school math—all while intensively building their biblical worldview and problem-solving skills. When finished, students will be ready to jump right into algebra, understanding both what algebra is about, why it’s important, and how it points to the Creator. There’s even an optional eCourse component available.

The program will help you transform your math class, show students why math (including algebra, geometry, trigonometry, and probability) matters, help students understand the mechanics of math, and leave students awed at God’s faithfulness.

### Algebra and Geometry Curriculum

I’ve always had a high regard for Jacob’s high school math series, and was excited when I saw they were being reprinted. I love how this program incorporates history and teaches the student to use math in problem-solving situations. Students won’t be left wondering what all those xs and ys or geometric proofs are about anyway. Instead, they’ll learn to apply the skills their learning and truly think mathematically. While the program doesn’t connect math to God, it does teach math as a practical tool. If students have already completed Principles of Mathematics, they should be able to see how what they’re learning declares the Creator’s praises. There are also DVD lessons available to help with mastering the skills.

## Math Curriculum Has Arrived

The second book in Principles of Mathematics series is now complete! I’m super excited, not only because it is done, but also because it’s my hope that this material will help students see God’s handiwork in mathematics and realize to a deeper level what an amazing, faithful God we serve. Many students (myself included years ago) wonder why they have to bother learning math (especially when it comes to algebra and other upper-level concepts). This curriculum answers that “why” question, equips students to use math in their own lives, and encourages them that they can trust God completely.

I’ve posted some sample lessons so you can “see” the curriculum.
* View textbook sample.
* View teacher guide/workbook sample.

There are also more details and a way to purchase it at the link below.

https://www.christianperspective.net/product/principles-of-mathematics-biblical-worldview-curriculum-year-2

The curriculum is designed as a full prealgebra curriculum (grade 7 or 8), but would also work well for older students seeking to understand math’s real purpose.

(If you know of anyone who might be blessed by this curriculum, please pass along the information. I’d also love to hear your thoughts, so please leave a comment below.)

## It’s Here! New Biblical Math Curriculum – Plus Video and Upcoming Events

It’s still hard for me to grasp the reality that it’s actually done. Writing this math curriculum has been an amazing journey, fraught with unexpected delays (such as a concussion that left me unable to work much on it for more than a year) and challenges. Yet as I look back, I see God’s provision each step along the way.

Thank you, dear readers, for being a part of that provision—for your prayers and your encouragement. I can’t tell you how much it has meant to me. (And please don’t stop praying! I’m still working on Year 2…which is due to come out late this year/early next.)

We decided to extend our pre-order pricing for a little longer, so you can still grab the curriculum at a reduced price you’d like a copy.

Also, I’ll be speaking at a couple of upcoming conventions and would love to see you there (I’ll be at the Master Books booth).

Here are the details:

Virginia – HEAV’s Virginia Homeschool Convention
June 11-13, 2015

Arizona – AFHE Home Education Convention
July 10-11, 2015

As you begin planning for next fall’s school year, don’t let the thought of math scare you. Math is a way of describing God’s creation—it’s a testimony to His faithfulness, wisdom, and greatness. If you haven’t seen it yet, check out this short video I made a couple years ago for a quick reminder of how math can be seen from a biblical worldview. This version includes an ending I recently added that offers a quick overview of the curriculum too.

## Review: Make It Real Volume 2 – And a 25%-Off Coupon Code at Make It Real Learning

Some time ago, I reviewed Make It Real Activity Library, Volume 1. Recently, they released a volume 2. Volume 2 is very similar to volume 1; once again, I appreciated how the series, designed as a curriculum supplement, provides numerous, stand-alone, real-world application problems for students. The series does not claim to be Christian, so Christian parents/teachers will want to discuss some of the lessons with their students, examining how we interpret the results or topic in a biblical worldview. Again, please see my previous review for more thoughts, as well as for a 25%-off coupon code good on all of the publisher’s products through the end of 2012.

Note: I received a free copy of this product to review. See my review policy disclosure.

## Mammoth Math Curriculum – And Free Worksheet Generators

Note: Please see these general guidelines and thoughts to help you as you choose math curriculum. Please also see our review policy disclosure, which is to comply with FTC regulations and explains our review policy.

I recently had the opportunity to review the Mammoth Math curriculum–a unique curriculum with lots of options (you can purchase it by grade or by concept, and it comes as either a download, physical CD, or printed material). Its flexibility could make it a good fit for those looking for a way to review or teach a specific concept or for a flexible textbook approach.

Whether you’re looking for a curriculum or not, you may want to check out the wide variety of free worksheet generators Mammoth Math/HomeschoolMath.net offers. The generators cover concepts ranging from the typical (such as addition and fractions) to the more unusual (such as foreign currencies and scientific notation)–and they’re all quite customizable. The ones on foreign currencies especially might be a fun supplement to use alongside learning about different countries. You could even cut out the coins from the worksheets, making them into pretend money, and then set up an imaginary store and buy things in the foreign currency. Make it even more challenging by looking up the exchange rate and estimating the cost in U.S. dollars!

The site also offers a downloadable sample of the curriculum that includes a generous amount of materials (more than 300 pages) when you sign up for their newsletter or their “Math Mammoth Tour” (an e-mail a day for seven days on the curriculum).

I’ve put my entire review below. If you’ve used the product, please feel free to leave your thoughts in a comment!

Disclosure: I requested and received a free copy of this product to review. See my review policy here.

## Review of  Math Mammoth

Publisher: Math Mammoth (written by Maria Miller)
Curriculum series covers grades 1-6; worksheet series covers grades 3-8.
Price:
\$32/grade for the complete curriculum as a download; downloads on individual topics are available for less than \$7 each; worksheets only (no teaching text) and discounted bundle packages are also available. Print versions are available (prices vary) through LuLu.
Where to Obtain:
www.mathmammoth.com

Math Mammoth offers both a complete curriculum series for grades 1-6 (their Light Blue Series) and the same basic material arranged by concept (their Blue Series) for those looking for a workbook on a specific concept as opposed to an entire grade. They also have just worksheets without concept presentations for grades 3-8 available, although these Golden and Green series would be more suitable for tutors or classroom teachers than for homeschoolers.

The material is available in either a digital format (either downloadable or on a CD) or a printed format. The digital format cuts down on the initial cost, although you will need to print out the worksheets yourself.

This curriculum is designed to be extremely flexible—the author, a math teacher and homeschool mother from Finland, encourages users to use the books as a “framework,” spending as little or as much time as needed rather than focusing on finishing the entire book. In her “User Guide,” she explains that while some pages are filled with drill problems, parents only need to assign the number the child needs—even if that is only one half or two thirds of the total ones given (a suggestion I heartily echo, no matter what curriculum you use).

Each chapter covers a concept and includes an overview for the parents, a list of related online resources, and presentations and worksheets for the students. The author has also created online worksheet generators (see www.homeschoolmath.net/worksheets) parents can use to generate additional worksheets if needed (although there are an ample number of worksheets in the books themselves).

As far as content goes, I appreciate how the curriculum tries to explain concepts with understanding and brings in practical word problems or examples. The program also uses a lot of pictures to help students connect abstract numbers with real-life objects. I did not notice examples of math in science, historical information, or any mentions of the Lord. The program includes a lot of game suggestions and links as supplements. Parents will want to selectively use the links and supplement the material with more science and history examples, as well as bring in the biblical perspective. The program also contains a lot of problems for each concept, and I definitely would echo the author’s reminder to only use what you need.

I see the program’s greatest strength as an inexpensive way to review or teach a specific concept. For example, if your child is struggling with fractions, you could purchase the fractions material from the Blue Series and work through some of the pages. I know a mother who is using it that way and really liking it. Since the material comes as a download, you only need to print out what you need. It could also be a good fit for those looking for a flexible textbook approach.

## Make It Real Learning Activity Library

11/28/2012 Update: Make It Real Learning now has a Volume 2 as well. This post was originally a review of Volume 1, but I have added information on Volume 2, as they are very similar. Look at the bottom of the post for a 25%-off coupon good at Make It Real Learning through the end of December 2012!

I recently had the opportunity to review the Make It Real Learning Activity Library–a collection of e-books filled with practical worksheets that truly give students the chance to use math in real-life scenarios. While they do not come from a biblical worldview, their format lends itself to the parent picking and choosing which scenarios to use as well as discussing them further and could be a resource for those wishing to bring in practical examples.

I’ve put my entire review below. If you’ve used the product, please feel free to leave your thoughts in a comment!

## Review of  Make It Real Learning Activity Library

Publisher: Make It Real Learning
Grade Level(s): K-College (Volume 1)/K-Grade 3 (Volume 2); see first paragraph below.
Price: \$39.99/each volume of e-books (11 in each volume). Note: The publishers have offered a 25% discount (good through the end of 2012) for readers of this blog; this is not an affiliate code, and I do not get any commission on it. I am just passing it along in case any of you wanted to use it. To use the discount, enter christianperspective25 as the code during checkout at www.makeitreallearning.com.
Where to Obtain: www.makeitreallearning.com

Like its name implies, the Make It Real Learning series by Frank C. Wilson seeks to make math real for students, answering the question of “when am I ever going to use this?” Each volume in the series consists of 11 e-books, each one of which contains 10 real-world scenarios. The e-books range from one on fractions, percents, and decimals to e-books on more advanced topics such as geometry, algebra, linear functions, and quadratic functions. The majority of the e-books deal with upper-level concepts. The website offers a general mapping of lessons to grades for volume 2, although homeschool parents should be aware that most homeschoolers are not required to follow these standards* (many homeschool curriculums vary from them) and thus will want to look at the lessons to see if their student knows the needed skills.

Each real-world scenario stands on its own and can be printed and handed straight to the student. Duplicate worksheets containing answers (and often detailed solutions) are included. The formatting is professional and clean. The scenarios could be used as periodic assignments to both provide a refreshing break from everyday math lessons and to teach students to use math practically. The e-books do not typically present any of the math itself (so you will want to make sure your child knows the information needed to complete the scenario); they are designed for the student to apply what he has learned or is learning to real-life scenarios.

The scenarios themselves vary greatly. Some of them rank among the most excellent, well-thought-out activities I have encountered. For example, students will get to find the cost of keeping a pet (using real petsmart.com data), make cell phone comparisons and investment decisions, examine different pool designs, and understand the math behind various pieces of data all around us we take for granted. On the flip side, the books also include scenarios mentioning topics I found unnecessary, such as AIDS and teen pregnancy. I would plan on finding some great scenarios, but know that you also might find some you would not want to use or would want to discuss. Many of the topics, such as those on health or population issues, warrant discussions and explorations of a biblical worldview of that topic. Others, such as those that examine aspects of God’s creation (such as the phases of the moon or the order in sound waves) just need a reminder that God is the One who put this incredible universe together. Since the material comes as an e-book, you have the ability to select just the scenarios that will work for your family by screening them on the computer and printing only those you want when you want them.

The thing I loved about many of the scenarios is that, unlike a typical word problem, they really take the student into the scenario and let them experience the decision in a way few math books even approach. When used selectively, I can see them being wonderful ways to present math as a practical tool, especially in the high school years where textbooks focus more and more on abstract math.

## 25%-Off Coupon Code

The publishers have offered a 25% discount (good through the end of 2012) for readers of this blog; this is not an affiliate code, and I do not get any commission on it. I am just passing it along in case any of you wanted to use it. To use the discount, enter christianperspective25 as the code during checkout at www.makeitreallearning.com.

Disclosure: I requested and received a free copy of this product to review. See my review policy here.

* For information on homeschool laws by state, see www.HSLDA.org. This is not meant to be legal advice. Requirements vary state by state.