Imagine yourself, a week away from your big day. It’s your 5K race! Or your districts championship swim meet! Or your SAT you’re dreading to take! Whatever the situation, you will usually hear tapering as a word used for a rest period. But why does tapering work?
Mostly, tapering works because of rest. Now, if you’re on a track and field team, and practice ends early, you’re probably tapering. The reason it works is because it helps you get more rest and allows you to burn less calories, so when the day comes, you have a lot of energy for your 5K or half-marathon, or 4K. It works with swimming, too. As your muscles work out less, you are less likely to be sore after practice, allowing you to have a lot of energy at districts or states, or whatever.
Tapering also works in academic situations with your brain, too. If you’re taking some sort of standardized test, you’re still expected to do classwork, right? So how are we supposed to taper with our brains. The answer is usually in homework. Teachers often don’t assign homework when students have to take standardized tests. But what if you’re taking the SAT’s, where teachers will still give you homework? Tapering works as if you’re working your brain less. People don’t study as much towards the test and look to gain more sleep. They also never do last-minute studying. That way, like most tapering, you have energy for the test, and that energy can be used for ultra brainpower.
Whether it’s the SAT’s, a marathon, or a district race you’re preparing for, you need to taper. Tapering helps ease your muscles or brain so the next day, your energy levels are high. The energy converts into muscle or brainpower. Hopefully you win, whether on the test, in the pool, or on the tracks!
If you’re that recreational athlete at the grocery store, or that competitive athlete near the sports drink section, or the middle guys in the water section, it’s tough to choose sports drinks versus water. Each has their own benefits and disadvantages. How to choose? It is mainly based on your intensity.
First, water has big benefits over sports drinks. First, they have no sugar. This is a huge advantage already because of no sugar, so you can’t have a sugar crash or gaining instead of burning calories. The only disadvantage it as is that there are no special effects to the water, like electrolytes or other particles. Fortunately, there are some waters out there that do have electrolytes built in to the water, like Smart Water, that have things like electrolytes.
Next, sports drinks also have big benefits over water, too, like they are especially made for athletes that train hard. They replenish electrolytes and give you an extra sugar boost. However, the sugar may have its disadvantages. Since sports drinks have large amounts of sugar, you might gain weight rather than lose weight if that’s the effect you want.
Now, which drink is better. In my opinion, water should be drank by athletes who only exercise for 30 minutes a day, and mild workouts. Sports drinks should only be drank if the workouts you are doing are very rigorous or physically demanding. If not, then just stick to your tap water.
What is the highway
That decides where we go?
Is it the road we take
Is it the road we don’t take
Or is it both?
Is time already decided
For us or not?
Whether Schrodinger thinks we do or not
Or whether the cat is alive or dead
Does it matter at all in our lives?
What is the matter whether
I take both tracks
Yet I will only choose one?
All I know
Is that thinking is the way
That came up with it all,
Whether both paths or one.
Through time people have wondered where math originated. Others wondered how the basics were created. So people wondered whether they could create a program to strip arithmetic to its bare bones. Here are some stories:
David Hilbert was a German mathematician. Near his age of the early 20th century, there was a need for discovering the foundations of math, since there were paradoxes and inconsistencies, like 1/0. So, Hilbert tried to create a program so they could strip arithmetic to the minimum. He would try to make all things in arithmetic without any misconceptions, so they could solve some questions they never could have with other method. But it failed. David Hilbert would find the truth off of Kurt Gödel.
Kurt Gödel was also a German mathematician that also wanted to discover the bare bones of arithmetic. However, looking at Hilbert’s Program, he realized that the attempts were fruitless and published his incompleteness theorems. It states that we cannot discover everything about arithmetic through equations and formulas. It shook the world as we knew it, with the most shaking theorem ever written.
Even though we would love to find the true basis of arithmetic, along with David Hilbert, Kurt Gödel proved they would be fruitless. This theorem proved that some problems were unsolvable. It might have saddened some people, but it is a great discovery as a theory to attack unprovable theories.
Math is one of the most real-world subjects you’ll ever need. However, some things in math are very confusing, like how calculus work and what linear algebra is, and so on. But 0.9999.. = 1? How do you prove this theory, when there are more proofs to prove it wrong than right?
A concept is really important to prove this theory. First, there are infinitely many numbers between any number. Say you say 1/2. Well, there’s 0.51 and 0.501. Or there’s 0.50000000001. You get what I mean. But 0.999… doesn’t follow these rules. There are no decimals bigger than 0.999… but less than 1. This shows that 0.999… isn’t like the other numbers.If there isn’t a number between them, then 0.999… = 1.
There are other various proofs that 0.999… = 1. Like how 1/3 is 0.333…. and if you multiply 1/3 by 3 you get 0.999… or 3/3 or 1. There are other internet proofs out there that prove that 0.999… = 1. But mainly the reason is that it works. It doesn’t fail at any job. It can operate fine even with this.
So maybe there’s a proof out there that says no, but I have the evidence to say that 0.999… = 1. Through rules of numbers and fractions, 0.999… = 1, whether you think no or yes. But yeah, whether there’s a little something between 0.999… and 1 is debatable, which is why this question will be asked over and over again.
Our world today is filled with vivd images, colorful with many different shades of green, red, and grey (if you’re into that stuff). But where do these colors come from? What really happens when we see black against white? How do we tell between colors?
A really powerful sense of ours is the eye. Although it does help us see, understanding it is important to describe where all colors come from. White is light, and black is the absence of light. But how do we know that other colors, like pink, green, blue, and red exist.? The light is what really helps perceive different colors.
This prism is the reason why we see colors. The rainbow that reflects off is the example of all of the colors that are possible. This way, we know that colors are real.
Now differentiation between colors is through the light we see. If the shape you’re looking at is blue, the blue light shines into your eyes and now your brain knows it as blue. Same goes with all other colors. Some animals, though, cannot perceive some colors. Dogs cannot see red.Our man eye is one of the best at perceiving colors. But when you are colorblind, sometimes the difference between red and green is nothing.
Colors revolutionize what we see and helps us make choices in life. Our eyes are responsible for this great sight vision, and even though us humans may not be the smartest species out there, it seems like we can’t see the future coming ahead. If a species can see that, I will be surprised.
What’s (usually) after geometry but before precalculus? Trigonometry! Trigonometry is a brach of math that discusses the ratios between sides when you know the angles of triangles and vice versa. Trigonometry is all about triangles and their complex features.
First, we must talk about a fundamental theorem in trigonometry: the Pythagorean theorem. This states that the two shorter sides on a right triangle are squared and added, will the longer side, or the hypotenuse, squared. This principle brought trigonometry to life, and soon, more things were being discovered about right triangles, and soon people realized how effective they were.
There are three main trigonometric ratios that you need to know. The first is sine. If you take a sine of an angle of a certain amount of degrees, it will show you how big the opposite side is compared to the hypotenuse. Next is cosine. Similar to sine, if you take cosine of x degrees, it will show you how big the side that makes the angle (and s not the hypotenuse) compared to the hypotenuse. Finally, is tangent. If you take a tangent to a certain amount of degrees, it will show you how big the opposite side is compared to the adjacent side (either of them are not the hypotenuse).
Trigonometry was really the base of western mathematics and trigonometry is a real world concept that can help finding side lengths using angles and other things.There are a lot more topics in trigonometry, but if you are interested, study trigonometry. It can teach you a lot of stuff that is useful in different careers.