Introduction
INTRODUCTION TO PROOFS
"A geometric proof involves writing reasoned, logical explanations that use definitions, axioms, postulates, and previously proved theorems to arrive at a conclusion about a geometric statement."
https://plus.maths.org/content/origins-proof
1.) Deductive reasoning helps to further emphasize proof of a valid or invalid statement. Explain.
2.) The 23 definitions that Euclid wrote in his timeless textbook Elements describe geometrical terms such as "points, lines, plane surfaces, circles, obtuse and acute angles and so on". Research and find the definitions of four of these phrases.
3) Recall the ten common notions and postulates. Pick two of each and give visual examples of what they mean. For example, (may not be repeated): "The whole is greater than the part." The UK is not equal to the entire pie chart
Task
APPLYING GEOMETRY/PROOFS TO REAL LIFE SCENARIOS
"Geometry is essential for applied mathematics, and it is used in architecture and engineering fields. Its development was crucial in the development of modern mathematics. It can also make abstract mathematical concepts more clear."
https://www.reference.com/math/geometry-used-engineering-61cda8c8758634f6?qo=contentSimilarQuestions
1.) Civil engineers are required to understand "how to compute quantities, such as volumes, areas, lengths, curvatures and moments of inertia. Furthermore, they must know how to determine the spatial relationship among shapes." Could these terms ever be used in a proof? Explain which ones and why or why not.
2.) "According to Teachnology, geometry has numerous practical uses in daily life." What jobs require a backround or involve/need geometry? Sports?
3.) "For example, in engineering projects, the concept of perimeter is used to compute the amount of material needed for a specific project." How could a simple proof problem be used for this scenario?
Process
HISTORY
http://www.math.wustl.edu/~sk/eolss.pdf
1.) Early geometry focused on things such as land surveying. What peoples inquired on such things? Why?
2.) "Heuristically, a proof is a rhetorical device for convincing someone else that a mathematical statement is true or valid." Does this definition still apply to the proofs we more commonly see today? Describe why or why not.
3.) Thales, Theaetetus of Athens, and Eudoxes all formulated actual theorems. Research these theorems and state why they are or are not presently used.
http://faculty.csuci.edu/roger.roybal/teaching/fall08/math331/P1_246.pdf
1.) "Although it may seem like a nuisance, proofs have saved us from a number of incorrect theories posed by amateur mathematicians." Research and find what mathematicians have been wrong in their studies.
2.) The Chinese developed their own proofs such as the pythagorean theorem. What is the pythagorean theorem?
3.) There are many advantages and disadvantages to using proofs. Compare and contrast.
Evaluation
Conclusion