Question

How many points are there on a taxicab circle with radius 4?

22

16

18

20

My answer: 16

Answer 1

@jim_thompson5910 @mathstudent55

Answer 2

in `taxicab geometry`, you can only move about on the integer coordinates. You cannot move in the space between the integer coordinate points because those spaces represent houses where the taxi can't drive

anyways, a `taxicab circle` is where all points are equally distant from a fixed point.

In this example, the red points are all equally distant from the blue point

https://upload.wikimedia.org/wikipedia/commons/thumb/d/de/TaxicabGeometryCircle.svg/214px-TaxicabGeometryCircle.svg.png

it turns out that there are 16 points shown and the radius is 4. So you are correct

Answer 3

when I say "distance" I mean the distance the car drives

you cannot move diagonally

Answer 4

In that latest screenshot, I show 2 points being 4 spaces away from the blue point

Answer 5

Alright, this one was confusing me but I think I got the answer. Complete question with drawing is here: http://prntscr.com/bchtsy

Rectangle ABCD is a golden rectangle. What is AB if BC is 10?


6.2
–16.2
5.4
4.8

My answer: 6.2

Answer 6

We can't have a negative length, so cross off choice B

Answer 7

BC is 10

AB is some length smaller than 10 (based on the answer choices I see)

Answer 8

The golden ratio is approximately 1.61803399

Answer 9

the idea is that we divide the length and height to get 1.61803399

Answer 10

BC/AB = 1.61803399
10/AB = 1.61803399
10 = 1.61803399*AB
1.61803399*AB = 10
AB = 10/1.61803399
AB = 6.18033988272398

which is approximately 6.2

Answer 11

so you got it correct

Answer 12

Wow I did not think I got that one right, but thanks. Okay, last one: http://prntscr.com/bchv49

I have no idea on this one because these graphs are really confusing me

Answer 13

Maybe 1 and 2, but I do not know

Answer 14

This is a tough one. A `Hamiltonian Circuit` is basically where you visit each node on a closed path. You start at one node, visit the rest, then come back to the starting node. You visit each node EXACTLY ONE time

Anyways, you just have to do this through trial and error. Here is what I came up with

Answer 15

So you're saying choices 2 and 3?

Answer 16

`An Euler path is a path that uses every edge of a graph exactly once`
Source: https://www.math.ku.edu/~jmartin/courses/math105-F11/Lectures/chapter5-part2.pdf

so in choice 2, we don't use path AC or CA
in choice 3, my screenshot isn't using path AC or CA

so choices 2 and 3 aren't euler paths

Answer 17

Oh okay, I get your point. I guessed on this one because I had no idea what to pick, but I think based on your explanation I got another question wrong. I check that one in a second.

Answer 18

http://prntscr.com/bchxzn

I chose Hamiltonian circuits for this one, but I do not think this is correct anymore :\

Answer 19

It seems like there are no Hamiltonian circuits or Euler paths

Answer 20

I agree with your answer

Answer 21

So I was correct with my initial answer?

Answer 22

yes

Answer 23

Thank you so much!! You are a wonderful helper.

Answer 24

no problem

Answer 25

The questions with the choices was incorrect for future references, it was actually choices 3 and 4 :)