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Mathematics in the World You Live In

It’s all connected. Math helps us understand better the world around us, from art to medicine to science. Math explains so much of it. Math has even been called the language of the universe. In short, God uses math all through His creation.  Therefore, it’s no surprise that humans use math in all they create as well.

In Algebra 1 we begin to understand ratios by starting out with fractions. We study spirals by understanding square roots.  Chapter 12 of our Algebra 1 course has especially fun square root illustrations with the horn of a ram for adding and subtracting square roots and the building of the Parthenon for dividing square roots. Here is a research article on how the Greeks used the Golden Ratio (often called the Divine Ratio) to build the Parthenon.  “This article will provide the best evidence I’ve found to date to illustrate appearances of golden ratios in the design of the Parthenon.” He has some really great illustrations in his article.

Art is used in our Algebra 1 Chapter 15  to show how the Golden Rectangle is used in famous artwork.  “The important relationship of mathematics to art cannot be understated when discussing Leonardo’s later work, and in numerous documents, letters and notes, the relevance of this is well documented. At times, he seems obsessed with these issues: while working on Mona Lisa for example, Leonardo is reported by Fra’ da Novellara to be concentrating intensely on geometry.”  – From this great article on Leonardo Da Vinci’s detailed math in his works of art as well as his scientific endeavors.

In Algebra 1 we learn how to manipulate numbers and use equations to find answers to real-life problems. Geometry takes those algebra skills and uses them to explain further how they can be used to draw, build, and even how math is abundant in nature.

Check out this fun article and see from hurricanes to dolphins to galaxies, we experience this amazing, and fittingly named, Divine Ratio.  Once we move into Algebra 2, Trigonometry, and Calculus we really see more fully the math come alive in the world around us.  How cool is it that we have the opportunity to understand it? Isn’t it awesome?

Let’s do some math! and never forget the big picture we’re learning toward.


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Homework Help Complex Problems – Moving Deeper into Concepts

As you move deeper into each textbook (Algebra, Geometry, Algebra 2 w/Trig, Calculus, etc), the problems will contain several concepts you’ve learned earlier – all in one problem.  This complexity can make it difficult to find the “how-to” or examples in the book to help us understand how to work it.

Recently, we received this question from our student support page: “There doesn’t seem to be any examples or teaching that I can find that helps me solve this problem.”

This is a common question – not this particular problem, but in general, as the problems develop into including several simple concepts stacked into compound calculations. However, the explanations are there, they just may be back a few, or several, chapters.

For example, Jacobs Algebra Chapter 12 Summary and Review Problem 14h.

Concepts include but are not limited to:

  • Chapter 12: Square Roots. Simplify radical as much as possible. Example of this step page 480-481
  • Chapter 5: Equations in One Variable. Specifically for this review problem, Equivalent Equations (Lesson 3) page 162-163.
  • Chapter 12: Square Roots: Radical Equations. Page 505 has examples of squaring both sides to eliminate the radical.

Math builds on itself. As you learn more and more concepts, the problems reach back and build on concepts and analyzing skills learned earlier in the book or even in an earlier course. These complex problems can be hard to find “how-to” when we just can’t see it! The solutions manual is a good resource to help with steps, but sometimes even with those steps, we need to see where it was explained or taught.

We are here to help! Send us your homework questions and let us help. Go to our support page for help. Be sure to include the 5 points below. These points make sure you’ve told us what we need to know to help you.

Be sure to tell us:

  1. the course,
  2. the chapter,
  3. the lesson,
  4. the problem,
  5. YOUR issue as best as you can explain it.

We love to help.