A neat way to calculate the area of a rectangle

I was sitting down, solving one of Catriona Shearer‘s geometry puzzles when I found this (by myself):

Look, I know it’s not the best of drawings, but it’s what I did.

If we call the long diagonal x, and the line segment perpendicular to the diagonal y, then the area of the triangle = xy/2, and the rectangle is made up of two of those triangles with area xy/2, so the total area of the rectangle = (xy/2) * 2 = xy.

I guess there could be another way to prove it. But this is the neat way I found!

peace

The uninteresting paradox

When I say uninteresting, I don’t mean that this paradox is uninteresting. It means “relating to the interesting/uninteresting numbers” and this is a paradox that is about uninteresting numbers.

When we say interesting number, they’re numbers with special features. Like 1 is the first positive integer, 2 is the only even prime, 3 is the first odd prime, 4 is the first composite, and so on. But what about uninteresting numbers?

If the list of uninteresting numbers went 7, 13, 35, 57, 89, 103, 205, 784, 1083, 1849, 3456, 8465, 9172, 10928, 40923, 98402, … then obviously 7 is interesting because it’s the first uninteresting number. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. (And on and on and on and on and on and on and on and on and on and on and on and on…)

Sorry about that, I just wanted to do it. So what it suggests is that, if the list is as above, then 7 can neither be interesting or the opposite (or it could be both, but what?) because to be interesting, it has to be the smallest uninteresting number (which 7 is), but that also implies that 7 is uninteresting, so it’s not one or the other, but either both or none.

Peace out.

The banana length puzzle

This is a puzzle from How to bake π by Eugenia Cheng, if you haven’t checked it out, make sure to do so. Here we go…


A rope over the top of a fence has the same length on each side, and weighs one-third of a pound per foot. On one end hangs a monkey holding a banana, and on the other end a weight equal to the weight of the monkey. The banana weighs 2 ounces per inch. The length of the rope in feet is the same as the age of the monkey, and the weight of the monkey in ounces is as much as the monkey’s mother. The combined age of the monkey and its mother is 30 years. Half the weight of the monkey plus the weight of the banana is a quarter of the sum of the weights of the rope and the weight. The monkey’s mother is as half as old as the monkey will be when it’s three times as old as its mother was when she was half as the monkey will be when it’s three times as old as its mother was when she was half as old as the monkey will be when it’s as old as its mother will be when she’s four times as old as the monkey was when it was twice as old as its mother was when she was a third as old as the monkey was when it was as old as its mother was when she was three times as old as the monkey was when it was a quarter as old as it is now. How long is the banana?

Trust me, it’s harder to type out the riddle than to actually solve it. The challenge was to do it mentally, but I found it too hard and I went on paper. The riddle looks long-winded (it is) and complicated, but it’s easier than its length. So basically, to summarize the italicized text, if the monkey’s age is ma and the mother’s age is mma, then

ma = 2/3 mma

or, the mother’s age is a half older than her son/daughter. With easy calculations, the monkey is 12 years old, 18 ounces heavy. The rope is 12 feet long, which is 4 pounds. That means that 6 + the banana’s weight in ounces = 22, meaning the banana is 16 ounces, thereby 8 inches.

BAM!

Disclaimer: I’m not sure if this is 100% accurate, but it’s good. 🙂 Good riddle, Eugenia Cheng!

TAU DAY!

Hello everybody!

I am proud to announce that today is TAU DAY! Yay!

Because it’s tau day, I’ll copy and paste 100 digits of tau:

6.2831853071795864769252867665590057683943387987502116419498891846156328125724179972560696506842341359

If you want to see 100000 digits of tau, figure out my puzzle!

(fastest Minecraft speedrunner on youtube capitalized)+(fastest Rubik’s Cube solver with space and Capitalized name)+(my favourite number)

good luck!

A secret hint

My first number is the same as the fifth

My last three numbers are an arithmetic progression with +1

My third digit is x, where 1/x is undefined

Subtract me from 0 and I am negative

Only one of my digits is a one

My second number is 9 (big hint)

My first is the square root of my favorite number

My favorite blog is the one with #youcanlearnanything spam

That’s like 5 hints

That’s my password for the next blog with a secret

PS it’s a six digit number LOL

PPS (or PSS?) you don’t need my favorite number

My new program

Recently, I made a program that detects prime numbers and non-prime numbers!

It’s very complicated!

Here it is!

Javascript:

function isPrime() {
   //all the variables
   var num = prompt("What is the number you seek?");
   var squarerooted = Math.sqrt(num); //defines the square root of num
   var primeTrue = false; // the true/false determiner
   var i = 2; //the first number to be divided into num
   var count = 0; //how many numbers below the square root of num divide evenly into num
   var Type = typeof num; //just a test
   console.log(Type); //just a test
   console.log(num);
   var finalOutput = "";
   //the test
   while (i<=squarerooted){
      if(num%i === 0){
         count++;
      }
      i++;
   }
   //determining the state of primeTrue : true or false?
   if(count === 0){primeTrue = true;}
   else{primeTrue = false;}
   //the final outputs
   if (primeTrue === true){console.log("PRIME"); finalOutput = "Prime";}
   else{console.log("NOT PRIME"); finalOutput = "Not prime";}
   console.log(finalOutput); // just a test
   document.getElementById("truefalse").innerHTML = finalOutput;
}

HTML:

<html>
 <head>
 <title>prime testing</title><style></style>
 </head>
 <body>
 <script>alert("1 is not prime, 0 is not prime, strings are not supposed to be prime.");</script>
 <button onclick="isPrime()">Try it</button>
 <p id="truefalse"></p>
 <script src="primetest.js"></script>
 </body>

</html>

Copy and Paste these code pieces into two separate .txt files and save the Javascript as (your choice).js and the HTML as (your choice).html

I’m sorry…

I forgot what I was going to write about! I’m SO SORRY! So instead, I will just do one I randomly pick.

79.7348327346834637534635243789238328324735495349027328526306538054360567057 second later…

I got it! I will be writing about my future BOOK!

My book will be called (I DON’T KNOW, OKAY?!?!) and it will be about math, obviously. It will probably review on the thing I wrote about, and possibly things I didn’t. It will be GREAT!

Hope to publish it!

P.S. It’s got great puzzles.