Algebra and Statistics Resources

While browsing the Internet today, I came across some fascinating videos that connected upper-level math concepts with real-life applications in an engaging, easy-to-understand way. The videos explore such varied examples as making fireworks and oil production–along with MUCH more!

The series are secular series, and I do not agree with some of the examples chosen and ideas presented in the videos, but they do contain very clear, helpful examples of math in action if you discern through some of the conclusions. It might be wise to discuss them together with your students afterward, and explore together what the Bible says about the various topics (the environment, health, etc.)

If you’re interested in the videos, I would suggest watching them soon, as the site dropped another video series on math they used to have, and purchasing the DVDs are VERY expensive. I think they rotate the content periodically.

Anyway, here are the links!

Algebra in Simplest Terms
Against All Odds: Inside Statistics

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Bridge-Building Resources (All Grades)

In my previous post on shapes, we briefly talked about how learning shapes doesn’t have to be confined to a textbook–how shapes help us understand and appreciate the shapes God placed around us.

Understanding how shapes respond to pressure–as well as lots of other math concepts–plays an important role in building bridges. Here are two bridge-building resources you could use with your children as a way to teach them to use math as a God-given, real-life tool.

Golden Gate Bridge – This section of the Golden Gate Bridge site offers lots of useful bridge-making links. There are links you could use with younger children, as well as ones for high schoolers.

Build a Bridge – While this interactive page doesn’t get into much of the math behind building bridges, it gives students an opportunity to explore the properties of different bridge designs and determine which design would be best suited for various situations.

Thoughts on Pi

Someone recently wrote and asked me if I had any information on pi from a Christian perspective I could share. So here are some thoughts on this mind-boggling–and incredibly useful–number.

What Is Pi?

Pi, symbolized π, is “A transcendental number, approximately 3.14159, representing the ratio of the circumference to the diameter of a circle and appearing as a constant in a wide range of mathematical problems.”[1]

As this definition explains, pi is a transcendental–a number that keeps going on and on. To get a better feel, take a quick look at the first 100,000 digits of pi–it’s a mind-boggling number!

Numbers such as pi defy our comprehension. As I mention in Revealing Arithmetic when looking at different types of numbers,

“The infinite nature of numbers reminds us of our limited knowledge. As James D. Nickel points out, ‘The infinite nature of the natural numbers has a way of telling man’s reason, ‘Under certain conditions, you can never know everything there is to know about me.'” Although our understanding is finite, God’s understanding is infinite. Psalm 147:5 tells us, ‘Great is our Lord, and of great power; his understanding is infinite.’ How foolish it would be not to trust Him!”[2]

When we look at pi, our minds should turn in awe and wonder at God’s greatness! Sadly, though, there “is almost a cultlike following that has arisen over the concept of π.”[3] It’s a reminder of Romans 1:20-23:

“For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, even his eternal power and Godhead; so that they are without excuse: Because that, when they knew God, they glorified him not as God, neither were thankful; but became vain in their imaginations, and their foolish heart was darkened. Professing themselves to be wise, they became fools, And changed the glory of the uncorruptible God into an image made like to corruptible man, and to birds, and fourfooted beasts, and creeping things.”

Has Pi Always Been Expressed the Way It Is Today?

Hardly! The symbol π is just a symbol man chose to help express that real-life ratio–the symbol has actually been used to mean other things! Like most math symbols, it has been adopted within the last several hundred years [4].

Throughout history, men have tried to more precisely define pi. I found it fascinating to read in π: A Biography of the World’s Most Mysterious Number that, when you really dig into the text, it appears the Bible accurately uses pi to the fourth decimal place (1 Kings 7:23)the book concluded that ”such accuracy is quite astonishing for ancient times.” [5] Not surprising considering the Bible’s Author!

Where Do We Use Pi?

Pi has a way of showing up all over the place–a testimony to the same Creator holding all things together. The most obvious use is when dealing with circles (for example, pi is used to find the area and circumference of a circle), but pi also proves useful in less-obvious places, such as in sound waves, general relativity, movements of the heavens, and probability, to name a few. 2018 Update: NASA has put together a Pi Day Challenge that shows just how useful pi is! Note that NASA does not come from a biblical worldview, so please use discernment (while most problems looked great, one at least hinted at finding life on other planets).

Why Are We Able to Explore Pi?

Because God created man in His image and gave him the ability to explore His creation! We’re thus accountable to Him for how we use that ability.

Where Can I Learn More?

There are lots of materials online that share more about pi (you might start with Wikipedia’s overview or this historical overview of pi). Your library may also have some books that could prove helpful. One I particularly enjoyed is π: A Biography of the World’s Most Mysterious Number by Alfred S. Posamentier and Ingmar Lehmanne.

The thing to keep in mind is to turn the wonder at pi itself into wonder at the Creator of all things–the one who understands what only baffles our comprehension.

Additional Thoughts (added March 2017)

Be careful when exploring pi to stand in awe of the Creator and not the creation itself. Throughout the years, men have been in awe of the number pi…yet that awe has often turned into an “almost cultlike following”[6] to the number instead of into awe of the Creator. To help put things in perspective, here’s a brief excerpt from Principles of Mathematics that explores pi, how it points us to the Creator, and how it’s been sadly twisted. http://www.christianperspective.net/wp-content/uploads/pi.pdf

 


[1] The American Heritage Dictionary of the English Language, New College Edition, 1980, s.v. “pi.”

[2] Loop, Katherine, Revealing Arithmetic: Math Concepts from a Biblical Worldview (Fairfax, VA: Christian Perspective, 2009), p. 125. Internal quote from James D. Nickel, Rudiments of Arithmetic: Foundational Principles in the Computation and Theory of Numbers, 1st ed. (preliminary draft) (U.S.: James D. Nickel, 2008), p. 294.

[3] Posamentier, Alfred S. and Ingmar Lehmann, π: A Biography of the World’s Most Mysterious Number (Amherst, New York: Prometheus Books, 2004), p. 13.

[4] It was “introduced in 1706.” Cajori, Florian, A History of Mathematical Notations: Two Volumes Bound As One (Mineola, NY: Dover Publications, 1993), vol. 2, p. 9.

[5] Posamentier, Alfred S. and Ingmar Lehmann, π: A Biography of the World’s Most Mysterious Number (Amherst, New York: Prometheus Books, 2004), p. 28.

[6] “There is almost a cult like following that has arisen over the concept of π.” Ibid., p. 13.

Thoughts on Shapes

Throughout history, men have used their knowledge of shapes to help them design buildings. Because of the consistent way God holds things together, we can predict how different shapes will hold up under pressure. One shape that supports weight well is the arch. You can easily see this by holding a piece of paper flat between your hands and having someone push down gently in the center of the paper. You should notice the paper bends easily under the pressure. But if you bend the paper to form an arch, you’ll notice the paper does not bend as easily. An arch shape holds up better under pressure than a flat shape does. [1]

Knowing this quality about arches helps us in designing buildings and bridges, many of which have an arch shape! It also gives us new appreciation for the design in our feet. If you run your finger along the bottom of your foot, you will feel multiple arches on your foot! God, the master engineer, designed the shape of our feet to support our body’s weight. Our feet are truly marvels of engineering!

If the foot were flat and rigid, fixed at right angles to the bone of the leg, walking would be difficult or impossible. The elastic arches also serve as shock absorbers to soften the jar resulting from walking on a hard surface.

The human foot is a miniature suspension bridge which is much more complicated than an ordinary bridge. Would anyone say that the Golden Gate suspension bridge just happened? Of course not, if he were truthful! But why do people assume that the even more intricate mechanism of the human foot could have just happened without intelligent cause or the workmanship of a master Engineer? [Allen L. Gillen, Body by Design (Green Forest, AZ: Master Books, 2001), pp. 43-44.]

The point? Learning about shapes doesn’t have to be confined to a textbook! As you teach your child shapes, you can be teaching him about the shapes all around us–and seeing the Creator’s wisdom and care in how He chose just the right shape for everything.


[1] This experiment is based on one given in The Art of Construction. The book offers numerous experiments and information related to building. Mario Salvadori, The Art of Construction: Projects and Principles for Beginning Engineers and Architects, 3rd ed. (Chicago: Chicago Review Press, 1990). Originally published as Building: The Fight Against Gravity.