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There’s a case to be made that the sharpest  object in the world can’t cut anything. Which seems weird, right? If you’ve ever sliced an apple with a  knife or sewn a badge with a needle, sharpness probably seems pretty straightforward.

If a tool is sharp…it cuts. Right? But, like most other things, scientists have  tried to pin down a way of measuring sharpness.

And the weird thing is, they haven’t  found a universal way to do it! There are a lot of ways to define sharpness  depending on what thing you’re trying to do. And those things could be important practices,  from surgery to scientific research.

And even if no one agrees on exactly how  to measure it, our search for better tools has recently led to some of the  sharpest objects we’ve ever created. [♪ INTRO] Before we get to the sharpest object in  the world, let’s start with the first thing that probably comes to mind when  you hear “sharp”: a knife blade. Part of the reason it sticks out as such a  vivid example is the distinct shape of a blade. Studying the exact details of that  shape, its geometric properties, gives us a starting point for defining sharpness.

The two sides of a blade’s edge  are usually straight and flat. And if we zoom in to the very edge, there’s a kind of wedge shape  where the two sides meet. Intuitively, the “sharpness” of the wedge  seems to come down to two main properties: how pointy it is and how narrow it is.

So, scientists have created specific  measures of “pointiness” and “narrowness”, to try and define sharpness! Starting with the former, if we zoom in  on the edge of a blade, called the “apex”, the tip of the wedge doesn’t shrink  to an infinitely small point. Instead, it ends in a tiny curve.

Think of that curve as forming part of a circle. The radius of that circle can  tell us how tight the curve is, which ultimately defines how  small the edge of a blade is. There's a word for this, it's called the edge radius, and it’s the geometric way we describe  the “pointiness” of a knife’s edge.

A smaller edge radius means a tighter curve,  closer to an ideal, perfectly pointy shape. But edge radius isn’t the whole story of sharpness because even blades with the same  radius can be thicker or thinner. So for “edge-radius” to be helpful, we first  have to pin down the “narrowness” part as well.

That’s defined by what’s called the wedge angle: the angle the between the  two flat sides of the wedge. A smaller angle means a thinner wedge,  which usually means a sharper blade. The upshot of all this is that  edge radius is only a helpful way of defining sharpness if the wedge angle is small.

In practice, that means  the things we call “blades” tend to be objects with wedge  angles of about 20 degrees or less. If we do have a small wedge angle, then edge radius is a helpful  start at determining sharpness. For instance, certain surgical scalpels  have sapphire blades with an edge radius as thin as 25 nanometers, which is  only a couple hundred atoms in width!

And with a blade that sharp, the scars left  behind by sapphire scalpels actually heal faster than steel scalpels thanks to the incredibly  precise, clean cuts it leaves in the skin. Plus, being made of hard sapphire and  all, the blades are also super durable. But even these ultra-sharp scalpels aren’t  the cutting edge of … cutting edges.

That title belongs to blades made of  obsidian, a kind of volcanic glass that can be crafted into an edge with  an edge radius just 3 nanometers across. That’s just dozens of atoms thick, making it one of the sharpest objects  we know of in terms of edge radius. Remarkably, we’ve been using these sharpest  tools as a species since the Stone Age!

And we still use obsidian blades today for  certain kinds of surgery, since their ultra sharpness means they can make cuts  without needing to apply much pressure. This is useful when you’re working on a  very delicate, fluid-filled part of the body like the eye, where we don’t want  to be poking into them too hard! In fact, obsidian blades are so sharp they  can even cut individual cells in half.

So in combination, edge radius and wedge  angle describe the incredible cutting power of obsidian pretty well. You might assume, then, that defining  sharpness is pretty cut and dry. Unfortunately, the geometric properties we’ve  discussed so far have some shortcomings.

Like, say, describing the sharpness of  needles and pins, which are also pretty sharp! Since they also come to a point at their tips,  we could use a radius, just as we did for blades. But unlike a blade, they don’t have  two flat sides that form a wedge, so wedge angle doesn’t really make sense here.

There are other kinds of angles we can  use, but they come with their own issues. With hypodermic needles, for instance,  there’s an angle between the slanted bit at the very tip and the straight edge of the  needle, which is called the “bevel” angle. You might assume that a larger  bevel angle means a sharper needle.

But the weird thing is, that’s not always true. One 2012 study in the Journal of  Diabetes Science and Technology found that having multiple bevel angles  on the same needle improved its ability to pierce skin, which is important for  making them less painful and more effective. As for edge radius, it isn’t always the most  sensible way to think of sharpness either.

For instance, the smallest radius  we’ve ever achieved on a man-made tool belongs to a tungsten nanoneedle, created  by scientists at the University of Alberta. It’s a super-thin structure that produces a tiny electrical current that jumps  between the needle and a surface. By doing so, the needle tip can identify  the positions of individual atoms on the surface and help us build up a  picture of what the material looks like.

And that tip is, wait for it, just one atom wide. You cannot get any tinier than that! It’s because of this ridiculously small  radius that the Guinness Book of World Records declared the tungsten nanoneedle the  sharpest human-made object in the world.

Which is cool and all, but  as we said in the beginning, there is one small problem: the  needle can’t cut or pierce anything! As you might imagine, an object just  one atom thick is incredibly brittle, so that super “sharpness”, if we can call it that, doesn’t improve the cutting power,  or poking power, of the needle. It would snap as soon as we tried  to apply any pressure to it.

That’s not just a problem  for tungsten nanoneedles. Even those obsidian surgical scalpels we  mentioned earlier aren’t used all the time because they’re also brittle and risk  breaking apart if a surgeon isn’t careful! So when it comes to how easy  something is to cut or pierce with, wedge angle and edge radius aren’t  the whole story behind sharpness.

They only describe the geometry of an  object, rather than its functionality. We can actually turn this around  and think about defining sharpness in terms of how easy something is to cut  with, which leads to a mechanical definition. Specifically, we can define sharpness in terms of the amount of  force we need to cut something.

For instance, those obsidian scalpels we  mentioned, they needed less pressure to make a cut into skin than a traditional steel scalpel, and that  same property crops up for other blades, too. One 2007 study by researchers at University  College Dublin attempted to measure the sharpness of a blade cutting into  soft materials by measuring how deep a given blade has to “poke” into the  material before it initiates a cut. The researchers showed that distance  reflects the amount of force you need to apply with a blade in order to cut.

Basically, if you don’t need much  force and only have to press a little, that’s what defines a sharp blade. This makes a lot of sense based  on how we think of sharp knives in the context of activities like cooking. Better still, the same researchers found that  the familiar geometric properties of blades were correlated with this  alternative definition of sharpness.

Other studies have found similar results,  connecting the wedge angle and edge radius definitions of sharpness to a lower amount  of force needed to cut with a given blade. That includes those stone-age  tools we mentioned earlier. A 2022 study led by an archaeologist at the  University of Cambridge found that stone tools with a smaller edge radius needed less  mechanical force to cut a PVC pipe.

So for stone tools at least, both the geometric and mechanical  definitions of sharpness make sense. But even if we use both definitions, there’s still something missing  from our picture of sharp tools. As it turns out, the mechanical  force needed to cut a material depends on what that material is!

We can’t just focus on the tool itself. A 2018 study by Italian researchers at  the University of Parma demonstrated this using a measure of sharpness that  incorporated both the geometry of the tool and the material properties  of the thing being cut. In the study, they used both a brittle,  polystyrene plastic and a soft, silicone rubber.

The sharpness metric behaved  as expected in the polystyrene, with narrower tools needing less force to  initiate a cut and form a crack in the material. But with the softer rubber, the shape  of the blade didn’t matter much. The force needed to make a cut  was really similar for the blades that the researchers defined as  “sharp” and “blunt” for that material.

That’s because unlike a brittle one, softer  materials have to be “squished into” a lot more before a cut starts to appear, and that  “squishing”, which researchers call “large deformations” follow the broader shape  of the tool rather than just the very very edge. So “sharpness” depends on the  thing you’re applying sharpness to. And I’m sorry about this, but  it gets even weirder than that.

The mechanical definitions we’ve just talked  about broadly assume that only the forces and distances in the process  determine cutting sharpness. But that doesn’t always hold true either! The way you cut also determines  the apparent sharpness of a blade.

For instance, one 1996 study by researchers  at North Carolina State University found that increasing the speed of  scissor blades cutting a plastic film reduced the amount of force needed to cut it! They suspected that this was because the film  crinkled up and became harder to cut at slower speeds, while at fast speeds the material was  smooth and easier to cut for the same blade. Kind of like how cutting wrinkled up saran wrap is a whole lot harder than  slicing through a smooth sheet.

And a 2007 study by French researchers  found that when they used carving knives to cut into a foam that had similar properties  to meat, the angle at which the blade cut into the foam affected the amount  of force needed to cut into it.. All told, “sharpness” isn’t just about an  object's shape or how easily you can cut into something because the multiple  definitions don’t always overlap, and they interact with each  other in complicated ways. So how do we define how sharp a tool is?

How can we make a video about  the sharpest object ever? Ultimately, it depends on the thing you’re trying  to cut, and how you’re planning on cutting it. As well as the shape of the tool,  you have to consider everything from the speed, angle, and  the material of the object.

In other words, to make a tool sharp,  engineers have to stay pretty sharp, too. This SciShow video is supported by Linode,  a cloud computing company from Akamai. Linode provides you and your company  with solutions for cloud computing, storage needs, databases,  analytics and all that fun stuff.

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As a reward, I’m just going  to keep eating my apple. [♪ OUTRO]