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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 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.

(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.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.3: Solving Linear Equations
Problem 8E: Aerobic Power Aerobic power can be thought of as the maximum oxygen consumption attainable per...
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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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