(BONUS) Metamathematics is the study of mathematics itself using mathematical methods. When we evaluate a normal formula the output is just a number. If we evaluate a MetaFormula the output is a formula, thus its a formula for formulas. Lets see if you can study MetaFormulas for figurate numbers: #of sides Shape Explicit Formula Modified Explicit 7 : 8 K 3 5 4 6 Triangle Square Pentagon Hexagon Heptagon Octagon *** : K-gon n(n+1) 2 n(2n + 0) 2 = n² n(3n-1) 2 n(4n-2) 2 n(5n-3) 2 n(6n-4) 2 + 1 0 1 : MetaFormula ↑ MetaFormula f Fill in the box for the modified formula for the Heptagon and Octagon. Then use the Modified formula lumn and inductive reasoning to produce a MetaFormula using two variables K and n. If done successfull- ou have produced MetaFormula for figurate formulas. That is, for any value of K the MetaFormula wi tput the formula for any sided figurate number.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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(BONUS) Metamathematics is the study of mathematics itself using mathematical methods. When we
evaluate a normal formula the output is just a number. If we evaluate a MetaFormula the output is a
formula, thus its a formula for formulas. Lets see if you can study MetaFormulas for figurate numbers:
#of sides
Shape
Explicit Formula
Modified Explicit
7
8
:
K
6
3
4
5
Triangle
Square
Pentagon
Hexagon
Heptagon
Octagon
:
K-gon
n(n+1)
2
n(2n + 0)
2
n(3n-1)
2
n(4n - 2)
2
n(5n-3)
2
n(6n-4)
2
1
3
42
1
+-n
-
1
NIN
2
MetaFormula ↑
MetaFormula f
Fill in the box for the modified formula for the Heptagon and Octagon. Then use the Modified formula
column and inductive reasoning to produce a MetaFormula using two variables K and n. If done successfully
you have produced MetaFormula for figurate formulas. That is, for any value of K the MetaFormula will
output the formula for any sided figurate number.
Transcribed Image Text:(BONUS) Metamathematics is the study of mathematics itself using mathematical methods. When we evaluate a normal formula the output is just a number. If we evaluate a MetaFormula the output is a formula, thus its a formula for formulas. Lets see if you can study MetaFormulas for figurate numbers: #of sides Shape Explicit Formula Modified Explicit 7 8 : K 6 3 4 5 Triangle Square Pentagon Hexagon Heptagon Octagon : K-gon n(n+1) 2 n(2n + 0) 2 n(3n-1) 2 n(4n - 2) 2 n(5n-3) 2 n(6n-4) 2 1 3 42 1 +-n - 1 NIN 2 MetaFormula ↑ MetaFormula f Fill in the box for the modified formula for the Heptagon and Octagon. Then use the Modified formula column and inductive reasoning to produce a MetaFormula using two variables K and n. If done successfully you have produced MetaFormula for figurate formulas. That is, for any value of K the MetaFormula will output the formula for any sided figurate number.
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