Superlesson Project 2-2
Geometry
Chapter 2, The Foundations of Geometry
When we refer to the Bill of Rights, we are usually talking about the first ten amendments to the United States Constitution. However, many organizations have their own bills of rights. Below, you will examine the bills of rights of the United States and of the real estate industry by analyzing the significance of assumptions and undefined terms within these documents.
Part A, Undefined Terms and Definitions
1. Look at Amendment VIII of the Bill of Rights of the United States.
a. Although the words used in the amendment are not defined within the amendment, most have simple definitions that most English-speaking people will understand. Which words and phrases in the amendment are unclear in their meanings?
b. How could these unclear meanings lead to legal arguments?
c. What assumptions are made in this amendment?
d. How could a lawyer logically argue that Amendment VIII of the Bill of Rights was violated if her client was sentenced to 100 hours of community service for vandalizing a street sign? Do you think she would get very far with this argument? Explain.
e. The last line of Amendment V reads "...nor shall private property be taken for public use, without just compensation." Rewrite this as an "if-then" statement.
f. Can this sentence be rewritten as a biconditional? If so, rewrite the sentence, or else explain why it cannot be done.
Part B, Postulates
2. The mathematical symbol "=" is roughly equivalent to the word "is." For example, the phrases "He is nice." and "Nice is he." both convey the same meaning (One just sounds a little odd!). This property is called the symmetric property. Because of it, you can use properties of equality to rewrite sentences that contain the word "is." (Note: Other forms of the verb "to be," such as "am," "are," and "shall be," are also symmetric.)
a. Read Article I of the United States Constitution. Use the symmetric property to rewrite the first phrase of the sentence.
b. Find another sentence in the Constitution that you can rewrite using the symmetric property.
c. Write a sentence that uses the reflexive property.
d. Pick another property and write a pair of sentences that illustrate it.
Part C,Working in a Deductive System
3. Like Euclid, the framers of the Declaration of Independence began with self-evident truths from which they built a system of laws. Euclid's geometry was based on postulates and undefined terms; the Declaration of Independence and, in turn, the United States government, are based on assumptions about human nature that are presumed to be universal.
a. Read the Declaration of Independence. What were the framers' self-evident truths?
b. What are some laws based on these truths?
c. What were the self-evident truths on which Euclid built his system of geometry?
d. The next document you will examine is the Real Estate Bill of Rights. Read the "To Account" section describing the agent's duties. Which words and phrases are undefined?
e. What assumptions are made in this section?
f. Describe a situation where the "To Account" section of the Real Estate Bill of Rights could be interpreted differently by the agent and the client.