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lapo4ka [179]
3 years ago
10

A regular polygon has an odd number of sides. Which statement is true about the lines of reflection for the polygon that will ma

p the shape onto itself?
A.
Lines that connect pairs of opposite vertices are lines of reflection.
B.
The perpendicular bisectors for each side are the only lines of reflection.
C.
The lines of reflection are parallel to the sides of the polygon.
D.
There are no lines of reflection.
Mathematics
1 answer:
Novosadov [1.4K]3 years ago
6 0

Answer:

The only correct option is:

Option B. The perpendicular bisectors for each side are the only lines of reflection.

Step-by-step explanation:

A regular polygon has an odd number of sides. Which statement is true about the lines of reflection for the polygon that will map the shape onto itself?

A.

Lines that connect pairs of opposite vertices are lines of reflection.

B.

The perpendicular bisectors for each side are the only lines of reflection.

C.

The lines of reflection are parallel to the sides of the polygon.

D.

There are no lines of reflection.

The only correct option is:

Option B. The perpendicular bisectors for each side are the only lines of reflection.

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Step-by-step explanation:

Earlier this month, news broke of progress on this 82-year-old question, thanks to prolific mathematician Terence Tao. And while the story of Tao’s breakthrough is good news, the problem isn’t fully solved.

A refresher on the Collatz Conjecture: It’s all about that function f(n), shown above, which takes even numbers and cuts them in half, while odd numbers get tripled and then added to 1. Take any natural number, apply f, then apply f again and again. You eventually land on 1, for every number we’ve ever checked. The Conjecture is that this is true for all natural numbers.

Tao’s recent work is a near-solution to the Collatz Conjecture in some subtle ways. But his methods most likely can’t be adapted to yield a complete solution to the problem, as he subsequently explained. So we might be working on it for decades longer.

The Conjecture is in the math discipline known as Dynamical Systems, or the study of situations that change over time in semi-predictable ways. It looks like a simple, innocuous question, but that’s what makes it special. Why is such a basic question so hard to answer? It serves as a benchmark for our understanding; once we solve it, then we can proceed to much more complicated matters.

The study of dynamical systems could become more robust than anyone today could imagine. But we’ll need to solve the Collatz Conjecture for the subject to flourish.Earlier this month, news broke of progress on this 82-year-old question, thanks to prolific mathematician Terence Tao. And while the story of Tao’s breakthrough is good news, the problem isn’t fully solved.

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Y + 4/9 = 2/3

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