Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

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#1 Re: Jokes » One liners - 218 » 2023-03-03 06:19:33

I can't seem to load

Does it work for you?

#2 Computer Math » Interesting Software Tools for Computer Math » 2023-01-25 11:43:29

Replies: 1

Today 666bro sent me an email asking

666bro wrote:

I'm intended to learn mathematical softwares especially open source one which is the good one to start with?

Here is what I wrote back:

Here are some tools you could try learning. They are related to mathematics but they are very very different things.

(1) R for statistics: This is a useful tool for making plots and graphs for your data.
(2) Sage for computer algebra: This is a swiss army knife tool - equivalent to mathematica. Tutorial should give you some idea of what you can do with it.
(3) Lean for verified proofs: In Lean, you can write the proof of a theorem and get the computer to check that your proof is correct. Check out Learning Lean and especially the "Natural Numbers Game".
(4) Z3: Z3 is a general purpose reasoning tool that can be used to solve puzzles or check large scale formulas written in a certain language. Tutorial

#3 Re: Euler Avenue » What do you think is the worst way to learn mathematics? » 2022-10-10 06:44:54

Do lay-people really teach themselves mathematics using Bourbaki books?

#5 Re: Dark Discussions at Cafe Infinity » What interesting apps/webapps have you come across recently? » 2022-01-16 17:36:09

Yes, Quora is very interesting. I spend a lot of time on Quora.

Have you heard of Nebula? It is a website where creators upload youtube style videos. However, it is not open to all like youtube, only invited creators post content.

#6 Dark Discussions at Cafe Infinity » What interesting apps/webapps have you come across recently? » 2022-01-11 15:54:12

Replies: 8

Here is a list I have:

1. Notion
2. Slowly
3. What 3 Words

What have you found?

#7 Coder's Corner » Tic Tac Toe with Haskell and Crash Course » 2022-01-11 15:51:01

Replies: 0

Hello all;

Please check out my Tic Tac Toe Tutorial with Haskell.

I also have 7 lecture crash course:

#8 Re: Maths Is Fun - Suggestions and Comments » Do the Administraters ever ask for help? » 2021-08-17 11:57:25

That is interesing. I am glad that the administrators have a growth mentality and are trying to learn new things. This certainly makes for a great morale in this community. smile

#9 Re: Maths Is Fun - Suggestions and Comments » Do the Administraters ever ask for help? » 2021-08-09 07:42:14

jabah013.307 wrote:

I have been questioning for ages but can it be possible for an Administrater to ask help from the Members and the Real Members? I have been reading all the posts but not even one administrater has even asked for help.

That is an interesting observation. I guess this either means that the administrators are not really hunting problems in the wild, or that they do not believe that members of this forum will be able to help them in what they need help with.

#10 Re: Help Me ! » A challenge for Coders/programmers » 2021-02-02 06:08:40

There are an infinitude of pairs (x,y,z). How can we brute force all of them?

#11 Re: Help Me ! » Probability » 2021-02-02 06:06:39

Probability is one of those things where it is very easy to convince yourself of something which is not true. I strongly suggest working out every step with full rigor.

Please explain with an example.

If you have a specific thing that you'd require clarification on, please post that.

By the way, I received your message on keybase. And I sent a reply.

#12 Re: Coder's Corner » Basic Common Lisp » 2020-09-16 03:58:07

Hi pi_cubed;

I am a big fan of functional programming myself.

Have you taken a look at Haskell? I suspect that you might find this language way more interesting and elegant!

#14 Re: This is Cool » Formal Methods in Mathematics / Lean Together 2020 » 2020-07-03 12:38:57

I am glad you asked. I think a good start would be to look at the Software Foundations book. Volume 1 is very interesting. You can download Coq and start working through it.

Kevin Buzzard, a mathematician who is very interested in formal methods is also working on a Natural Number Game. I have not played this game myself, though.

As for prerequisites, some experience with coding and logic will help.

#15 Re: Euler Avenue » Would certain 3D objects be viewed as impossible in 4D? » 2020-07-03 12:36:15

Bob Bundy,

the impossible cube and the hypercube are different examples, right?

#17 Re: Euler Avenue » Would certain 3D objects be viewed as impossible in 4D? » 2020-07-03 01:37:06

pi_cubed wrote:

Certain 2d objects, such as the penrose triangle, are possible in 2d but not in 3d. My question is, are certain 3d objects impossible in 4d, and what are they?

There are no nontrivial knots in 4 dimensions. so any way you twist a piece of string and glue it in 4 dimensions, it can be unknoted.

#18 Re: Maths Is Fun - Suggestions and Comments » This forum has been really inactive lately... » 2020-07-03 01:33:06

I posted a thread about "Formal Methods in Mathematics" but nobody seemed to be bothered

#19 Re: Dark Discussions at Cafe Infinity » Who was Anthony R. Brown? » 2020-07-03 01:29:40

Mathegocart wrote:

He's (most likely) mentally ill. He posts on about his chess engine on Youtube, which only works by SEVERELY handicapping Stockfish.

Also, I published a topic about his recent behavior.

Hmm, you found the wrong guy on twitter

#21 Re: Introductions » Hello from Maine, USA » 2020-07-02 01:18:50

Looks like the mods have cleaned it up

#23 Re: Dark Discussions at Cafe Infinity » Who was Anthony R. Brown? » 2020-06-30 13:02:08

"who is ARB" is a question which I used to find absolutely fascinating when I was a teenager.

#24 Re: This is Cool » Miscellany » 2020-06-30 13:00:09

ganesh wrote:

581) Lizard

Lizards are reptiles. There are over 4,675 species of lizard, according to the San Diego Zoo. Others sources say there are about 6,000 species. Included in this large number are lizards with four legs, some with two legs and some with no legs at all; lizards with frills, horns or wings; and lizards in nearly every color imaginable.


Lizards generally have small heads, long bodies and long tails. With so many species of lizard, it's understandable that they come in a wide variety of sizes. The largest lizard is the Komodo dragon. It grows up to 10 feet (3 meters) long and weighs up to 176 lbs. (80 kilograms). The smallest lizard is the tiny dwarf gecko, which grows to 0.6 inches (1.6 centimeters) long and weighs .0042 ounces (120 milligrams).


Lizards are found all over the world in almost every type of terrain. Some live in trees; others prefer to live in vegetation on the ground, while others live in deserts among rocks. For example, the Texas horned lizard is found in the warm areas with little plant cover in southern North America. The northern fence lizard, on the other hand, likes to live in cool pine forests in northern North America.


Most lizards are active during the day. Lizards are cold-blooded animals, which means they rely on their environment to help warm their bodies. They use the heat of the sun to raise their body temperatures and are active when their bodies are warm. The sun also helps lizards produce vitamin D. Their days are spent sun-bathing on rocks, hunting for food or waiting for food to come their way.

Some lizards are territorial, while others can easily live with dozens of other lizards of many different species. Other than mating times, most lizards are not social, though. There are some exceptions. For example, the desert night lizard lives in family groups, according to research by the University of California.

A lizard's scaly skin does not grow as the animal ages. Most lizards shed their skin, or molt, in large flakes. Lizards also have the ability to break off part of their tails when a predator grabs it.


Many lizards are carnivores, which means they eat meat. A typical diet for a lizard includes ants, spiders, termites, cicadas, small mammals and even other lizards. Caiman lizards eat animals with shells, such as snails.

Other lizards are omnivores, which means they eat vegetation and meat. One example of an omnivore lizard is Clark's spiny lizard. These lizards like fruits, leaves and vegetables.

Some lizards are herbivores and only eat plants. The marine iguana, which lives in the Galapagos Islands, eats algae from the sea. Iguanas and spiny-tailed agamids also eat plants.


Many lizards lay eggs while others bear live young. For example, frilled lizards lay eight to 23 eggs, according to National Geographic, while some skinks have live young. The gestation for a lizard egg can last up to 12 months.

Most baby lizards are self-sufficient from birth and are able to walk, run and feed on their own. The young reach maturity at 18 months to 7 years, depending on the species. Some lizards can live up to 50 years.


Here is the classification of lizards according to Integrated Taxonomic Information System (ITIS):

Kingdom: Animalia
Subkingdom: Bilateria
Infrakingdom: Deuterostomia
Phylum: Chordata
Subphylum: Vertebrata
Infraphylum: Gnathostomata
Superclass: Tetrapoda
Class: Reptilia
Order: Squamata
Suborders: Amphisbaenia, Autarchoglossa, Gekkota, Iguanias, Serpentes

The suborder Dibamidae, with the genera Anelytropsis and Dibamus, may also be included, though ITIS says these categories have "uncertain position."

Conservation status

Lizards vary in their conservation status, much like their traits vary. Many, according to the International Union for Conservation of Nature's Red List of Threatened Species, are endangered or critically endangered, meaning they may be close to extinction. Some lizards that are critically endangered include Campbell's alligator lizard, St. Croix Ameiva, Frost's arboreal alligator lizard, Be’er Sheva fringe-fingered lizardand the Doumergue's fringe-fingered lizard.

Other facts

Frill neck lizards have a large, round collar of skin that pops up when they are trying to intimidate attackers.

The green basilisk lizard can run on water at about 5 feet (1.5 m) per second for 15 feet (4.5 m), or more according to National Geographic. Their special feet give them more surface area to hold them up and as they run, they create air bubbles that keep them afloat.

Chameleons' tongues are longer than their bodies, and their eyes can look in two different directions at once.

You can shine a light in a banded gecko's ear and the light will come out the other side, according to the American Museum of Natural History.

Two species — the Mexican beaded lizard of western Mexico and the Gila monster of the southwestern United States and northwestern Mexico, are venomous, according to Encyclopedia Britannica.

What do you think of Reptoid Humanoids?

#25 Re: Introductions » Hello from Maine, USA » 2020-06-30 12:57:09

What is your favorite color, Eric?

Do they have good seafood in Maine?

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