Make sure you build or generate at least five more Pythagorean Triples using one of the many formulas available online for doing this.
After building your triples, verify each of them in the Pythagorean Theorem equation.
The assignment must include (a) all math work required to answer the problems as well as (b) introduction and conclusion paragraphs.
Your introduction should include three to five sentences of general information about the topic at hand.
The body must contain a restatement of the problems and all math work, including the steps and formulas used to solve the problems.
Your conclusion must comprise a summary of the problems and the reason you selected a particular method to solve them. It would also be appropriate to include a statement as to what you learned and how you will apply the knowledge gained in this exercise to real-world situations.
The assignment must be formatted according the APA (6th edition) style, which includes a title page and reference page.
Example of how it needs to be done.
YOUR NAME HERE
DATE
ANSWERS MUST BE HIGHLIGHTED IN YELLOW
Hint: here is a fun resource to get you started! Be sure to review the many formulas available for generating Pythagorean triples:
http://en.wikipedia.org/wiki/Formulas_for_generating_Pythagorean_triples#Euclid.27s.2C_Pythagoras.27.2C_and_Plato.27s_formulas
Here is an example formula for GENERATING Pythagorean Triples:
Suppose that m and n are two positive integers, with m < n. Then n2 – m2, 2mn, and n2 + m2 is a Pythagorean triple.
(source: http://blog.dreamshire.com/project_euler/triples.html)
For instance, let’s pick the numbers m = 4 and n = 5.
So, our triple becomes:
a: 5^2 – 4^2 = 9
b: 2*4*5 = 40
c: 5^2 + 4^2 = 41
(9, 40, 41)
You are welcome to use the above formula for finding your triples, if you would like. If not, you can find a different formula of your choosing. ïŠ
An example of what NOT to do:
My triple is 9, 40, 41
92 + 402 = 412
81 + 1600 = 1681
Why is this incorrect? ïŠ Here, I am just listing the triple and checking it with the Pythagorean Theorem, a2 + b2 = c2. The assignment asks you to BUILD/GENERATE the triple using a formula that you find online, and then CHECK it using the Pythagorean Theorem.
Intro Paragraph:
(TYPE YOUR INTRO PARAGRAPH HERE)
Pythagorean Triple #1:
Build/generate a triple using one of many formulas available online. Please show your work. Note – please remember that using the Pythagorean formula ONLY does NOT constitute building or generating the triples. You must build/generate them using a different formula (such as the one above) and then CHECK to make sure that they form a triple by using the Pythagorean theorem, a^2+b^2 = c^2.
• The Triple is: ANSWER HERE
Check your work using the Pythagorean Theorem equation here.
Pythagorean Triple #2:
*Build/generate a triple using one of many formulas available online. Please show your work.
• The Triple is: ANSWER HERE
Check your work using the Pythagorean Theorem equation here.
Pythagorean Triple #3:
Build/generate a triple using one of many formulas available online. Please show your work.
• The Triple is: ANSWER HERE
Check your work using the Pythagorean Theorem equation here.
Pythagorean Triple #4:
Build/generate a triple using one of many formulas available online. Please show your work.
• The Triple is: ANSWER HERE
Check your work using the Pythagorean Theorem equation here.
Pythagorean Triple #5:
Build/generate a triple using one of many formulas available online. Please show your work.
• The Triple is: ANSWER HERE
Check your work using the Pythagorean Theorem equation here.
Conclusion Paragraph:
(TYPE YOUR CONCLUSION PARAGRAPH HERE)
