How many holes does a donut have? That’s pretty easy: one. What about a straw? Two (one at each end) or just one? (Isn’t a straw just an elongated donut?) Does a coffee mug have one hole or two? Does a bowl have a hole? If no, then what about a hole in the ground or a hole in a wall that doesn’t pass all the way through? Does a basketball have a hole? A Reddit user asked 1600 people how many holes were in various objects and the results are fantastically all over the place.
This is a trivial question, but it reveals something interesting about people’s perceptions. The dictionary definition of “hole” includes two main meanings for the purposes of this question: “an opening through something” and “a hollowed-out place”. Mathematics offers another possible meaning:
A hole in a mathematical object is a topological structure which prevents the object from being continuously shrunk to a point. When dealing with topological spaces, a disconnectivity is interpreted as a hole in the space. Examples of holes are things like the “donut hole” in the center of the torus, a domain removed from a plane, and the portion missing from Euclidean space after cutting a knot out from it.
Here’s my short answer that is also the reason I’m not an algebraic topologist. If you can put it on a necklace, it has a one-dimensional hole. If you can fill it with toothpaste, it has a two-dimensional hole. For holes of higher dimensions, you’re on your own.
That answer isn’t very satisfying. Is there a better way to describe holes? I talked with some of my topologist friends and discovered two things: topologists don’t all agree on what a hole is, and it’s fun and interesting to think about different interpretations of a word whose mathematical definition isn’t completely settled. I think my larger conclusion, in the spirit of the season, is that holes are like Santa Claus: the true meaning is in your heart.
No wonder those poll results are all over the place. But at the same time, it’s interesting that many more people say that donuts have a hole than washers or rubber bands. I guess donut holes have better marketing? As for straws — reason tells me they only have one hole but I know in my heart they have two. (via the whippet)
A hole is an opening in or through a particular medium, usually a solid body. Holes occur through natural and artificial processes, and may be useful for various purposes, or may represent a problem needing to be addressed in many fields of engineering.
A hole is a point on the graph where the value of the function is not defined. If the numerator and denominator of a rational function have a common factor, they will cancel when simplifying. The cancelled value creates a hole in the graph.
When dealing with topological spaces, a disconnectivity is interpreted as a hole in the space. Examples of holes are things like the "donut hole" in the center of the torus, a domain removed from a plane, and the portion missing from Euclidean space after cutting a knot out from it.
Removable discontinuities occur when a rational function has a factor with an x that exists in both the numerator and the denominator. Removable discontinuities are shown in a graph by a hollow circle that is also known as a hole. Below is the graph for f ( x ) = ( x + 2 ) ( x + 1 ) x + 1 .
The word hole comes from the Old English hol meaning "cave" which in prehistoric times wasn't just a dark space to hide, it was a home. The word hole is used in many contexts from a rabbit hole where rabbits live to "a hole in one" — the golf term.
Golfers must play a round of nine or eighteen holes, a golfer who successfully puts the ball in the hole on his tee shot has earned his hole in one. However, if a golfer gets a hole in one on the fourth hole, then rain comes and the course becomes unplayable, the hole in one will not be recognized.
an empty space in an object, usually with an opening to the object's surface, or an opening that goes completely through an object: dig a hole We dug a hole and planted the tree. hole in My jumper's got a hole in it. Drill a hole through the back of the cupboard and pass the wires through.
Assuming that the straw is a simple, closed surface with no self-intersections, it has one hole. This is because the straw can be thought of as a tube-like surface with an outer boundary (the rim of the opening) and an inner boundary (the inner rim of the opening), which forms a single hole.
In everyday language, we use “hole” in a variety of nonequivalent ways. One is as a cavity, like a pit dug in the ground. Another is as an opening or aperture in an object, like a tunnel through a mountain or the punches in three-ring binder paper.
To find the holes in the graph, look at the denominator factors that were cancelled. To find the coordinates of the holes, set each factor that was cancelled equal to 0 , solve, and substitute back in to x+3x−4 x + 3 x - 4 . Set x−2 x - 2 equal to 0 0 .
There are different kind of hole. A bottomless hole is one of them. Technically most holes have no bottom to them ie a hole in a wall. Holes generally go all the way through what they are a hole in.
Hole and whole are hom*ophones — words that sound the same but have different meanings. Hole is a noun that refers to an empty space, while whole is an adjective that refers to completeness. Here's a quick guide to their differences and a handy trick to remember them.
In common language, a hole is often thought of as having two sides— an entrance and an exit. However, from a more abstract or mathematical perspective, a hole can be considered the absence of material, making it challenging to attribute sides to it.
Introduction: My name is Kerri Lueilwitz, I am a courageous, gentle, quaint, thankful, outstanding, brave, vast person who loves writing and wants to share my knowledge and understanding with you.
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