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Are there any practical applications of pi, aside from calculating the area or circumference of a circle?

pi

Thank you to Linda Johnson from Walnut Creek for the question. Dr. David H. Bailey, co-discoverer of the Bailey–Borwein–Plouffe formula for pi, guest authored this post. Many presume that π is only used for geometric measurements, say to calculate the area of circle or its circumference. While such calculations are done many, many times every day in modern science and engineering, there are numerous other context and applications, some of them quite surprising, where π appears.

Are there more fractions or decimals?

Thanks to Anonymous 9th Grade Student for the question. This is actually a surprisingly deep question. When students are in elementary school, they are taught how to convert between the decimal and fractional representations of a number. 0.4 = 2/5. 0.33333333333...=1/3. 0.237 = 237/1000. So we might initially think that every decimal can be written as a quotient of integers and vise versa. (Integers are whole numbers and negative whole numbers: 4, -3, 25745, -342 and NOT 3.2) This would lead us to believe that there are as many fractions as decimals. We might also recognize that there are an infinite number of fractions and an infinite number of decimals. From there might assume there are the same number of each: infinity.

How do I know what changes California made to the national version of the Common Core?

Thanks to Felicity from Los Angeles for the question. The changes are fairly minimal, but it's important to know what they are. Click here for California's version of the standards. Standards unique to California are in bold and have "CA" written after the standard. For example, on page 129, two function standards have been added under "Interpreting Functions" making the total number of standards 11 instead of 9.

Where can I find quality resources to use with my students?

Thanks to Adam from Lindon for the question. When we find resources we like, we add links to them on our Math Resource Mapper. You can search for resources by standard and everything on the site is free. We'll be uploading new content regularly, so check back often.