Using Euclid's Propositions: 1. Prove that the regular octagon is constructible. 2. Prove that the regular...

Using Euclid's Propositions:

1. Prove that the regular octagon is constructible.

2. Prove that the regular decagon is constructible.

Expert Solution

Thanks

milcah answered 2 years ago

Which one of the followings is constructible by using compass and straightedge? Why A. regular 7-gon...

Which one of the followings is constructible by using compass and straightedge? Why A. regular 7-gon B. regular 37-gon C. regular 85-gon D. regular 97-gon

Prove that {anbamba2m+n:n,m≥1} is not regular using pumping lemma

Find the area of a regular octagon of side 10 cm. (NOTE: Do not use the...

Find the area of a regular octagon of side 10 cm. (NOTE: Do not use the directed formula of the area of the polygon)

1) a) Let k ≥ 2 and let G be a k-regular bipartite graph. Prove that G...

1) a) Let k ≥ 2 and let G be a k-regular bipartite graph. Prove that G has no cut-edge. (Hint: Use the bipartite version of handshaking.) b) Construct a simple, connected, nonbipartite 3-regular graph with a cut-edge. (This shows that the condition “bipartite” really is necessary in (a).) 2) Let F_n be a fan graph and Let a_n = τ(F_n) where τ(F_n) is the number of spanning trees in F_n. Use deletion/contraction to prove that a_n = 3a_n-1 - a_n-2...

Prove the following using the properties of regular expressions: (ab)* + c + c* = Λ...

Prove the following using the properties of regular expressions: (ab)* + c + c* = Λ + ab + (ab)* + c(Λ + c*) Λ+ab+abab+ababab(ab)* = Λ + ∅* + (ab)* a(b+c*) + (d+e)* = ab + ac*c* + d + e + (d+e)* a*b + a*a*bc* + d* + ab = d* + ab + a*bc* + Λ a(b+cd*) = a(b+c) + acdd* (a+b)* = ∧* + ∅* + (a*b*)* (ab)*(c*+d*) = (ab)*(c+c*) + (ab)*( ∧ + d*)

Question 4 Prove that the following language is not regular. ? = { 0 ?1 ?...

Question 4 Prove that the following language is not regular. ? = { 0 ?1 ? | ?, ? ≥ 0, ? ≠ 2? + 1 } Question 5 Prove that the following language is not regular. ? = { ? ∈ { 0, 1, 2} ∗ | #0 (?) + #1 (?) = #2 (?) } where #? (?) denotes the number of occurrences of symbol a in string w.

Prove that {0n1n2n:n≥1} is not a regular language. The decimal notation for a number is the...

Prove that {0n1n2n:n≥1} is not a regular language. The decimal notation for a number is the number written in the usual way, as a string over the alphabet {0,1,⋯9}. For example, the decimal notation for 13 is a string of length 2. In unary notation, only the symbol “I” is used; thus 5 would be represented as IIIII in unary notation. Show that each of the following is or is not a regular language. (For regular languages, write down its...

Question