DorFuchs- deutscher Musiker-Mathematiker: (AKA- How to multiply two digit numbers in your head!)

Image result for dorfuchs multiplizieren

(Image from YouTube)


…And other cool videos. So, I was watching the videos of the awesome Vi Hart, one of my favourite mathematical YouTubers, the other day because I was late for Pi Day. (The link leads to Vi’s featured video Twelve Tones, about the musical constraint of using all twelve notes in a song.) Vi’s Pi Day videos are particularly interesting because usually they aren’t about celebrating Pi but its twice-multiplied, yet often-forgotten cousin, tau – more on which you can find in her videos.

Pi Day, for those of you who were unaware, is the 14th of March – because in the American calendar the number of the month (3, because March is the third month) is put in front of the day (the 14th) so 3(month)/14(day)/2017 – whereas in European calendars it is the other way around. (so Pi Day would be the 14th March, written as 14(day)/3(month/2017(year). And Vi Hart happens to be American, as well as the creator of Pi Day, Larry Shaw in San Francisco 1998. So they use the American calendar system. Which I guess is good for Pi, because there is no 14th month. It can have a whole day to itself.

Anyway -then I wondered if there were more mathematical YouTubers – and I came across DorFuchs. Like Vi, he is a ‘mathemusician’, who combines maths and music to teach people mathematical concepts.  After watching a few of DorFuchs’ videos I decided,’Tja, dieser Kerl gefallt mir’, and I went to see some more of his stuff! 🙂

One of DorFuch’s videos is a rap about multiplying two 2-digit numbers 11-19 in your head. At first I thought – ‘how?’ For example, how many people can answer this:

13 x 19 =

…in a few seconds  and completely ohne Tachenrechner – without a calculator?

Now watch DorFuchs’ video

Don’t worry, I’ll tell you what he just said.

So in the first few seconds, DorFuchs outlines the problem: Multiplying numbers is extremely useful, and multiplying one digit numbers such as 6×7 is super-easy. But multiplying 13 x19 for instance is so hard. But, he says ‘Lernen den folgene Trick’ – learn the following Trick – and  then you’ll probably be able to do it without a calculator! ‘Und dann schafft du dass veillicht sogar ohne Tachenrechner.’ (0:26)


Aber was ist das Trick?? DorFuchs singt es zu uns:


‘Nimm die erste Zahl, plus die letzte Ziffer von der zweiten.

Hang einer Null dran, und jetzt bist du bereit, denn

Wenn du das Produckt der letzten Ziffern addierst,

Dann bist du fertig und du werdest schneller wenn du das nochmal probierst.’-0:34

So I tried this out on a few numbers – of course I had to translate it first, just to check what DorFuchs was doing.

So: Nimm die erste Zahl, plus der lezten Ziffer von the imperative form of verbs. der zweiten.’ – Hmm, seems he’s using the Befehlsform or imperative forms of verbs – to tell us to do something. As mentioned here, the imperative is formed by taking the ‘stem’ of the verb’.

Nehemn – to take

Take the first number, plus the last digit from the second,

Hang a zero (0) next to it, and now you’re ready – then

When you add the product of the last units,

Then you’re finished – and you’ll be quicker when you try it again..


and so on.


Die Zahl – number     Der Ziffer-, digit

eine Null – a zero

das Produkt – product (the result of multiplying two numbers)

multiplizieren – to multiply

addieren -to add

probieren – to try

(notice ‘mal’ can mean both ‘again’, as in ‘Noch mal’ and ‘times’ as in 18 times 19 = 342)

As DorFuchs shows us, this trick always works with any number from 11 to 19.

13x 19, I hear you ask?


13 + 9 = 22 Nimm die erste Zahl, plus die letzen Ziffer von der zwieten

22 (*10)= 220  Hang eine null dran (bzw. mal zehn) und jetzt bist bu bereit, denn

+ (3×9=27) Wenn du das Produckt der letzen Ziffern addierst

220+27 = 247

Dan bist du fertig und du werdest schneller wenn du das immer mal trainierst.


(And just in case you want to check the answer, grab your Taschenrechner and check it out.)

Online Taschenrechner/Calculator


And at 1:06 – DorFuchs explains WHY it works.

‘Doch Achtung! – redet das Trick wirklich nur von Zahlen von elf bis neunzehn an?’ -1:14

an/reden – to speak of, to address.

Does the trick really only address numbers from eleven to nineteen? How can you change the song – aka the formula – to make it work for numbers from 21-29, or 31-39 or 71-79?  (That was an open question – comment away, those of you who are mathematically inclined. Meine Antwort befindet sich auf Englisch unten in den Kommentaren.)


‘Denn diesener gerade 10 plus irgendwie Ziffer von eins bis neun -okay.‘ – 1:18

Und wir rechnen ja jetzt – zehn plus a mal zehn plus b.‘ – 1:19

(10+a) * (10+b)

DorFuchs here makes the multiplication into a formula that can be true for all numbers from 11 to 19.

Any of these numbers is 10 (zehn) plus ‘irgendwie Ziffer’ – some digit from one to nine.

These unknown digits are called a und b (in English we pronounce it (Ay and Bee) – In German it’s pronounced (Ah und Beh) )

As ‘mal’ means ‘to times’ or ‘to multiply’, we are multiplying (10+a) x (10+b), so

(10 + (random number A)) mal (10+ (wahllosige Zahl B)).

1:23Das macht, wenn ich schon mal von Multiplizieren nichts übersehe,

(10*10 (+ (10*b) +(10*a) + (a*b)


DorFuchs comes to this conclusion by expanding die Klammern – like this

(10+a) *(10+b) = 10(10+b) + a(10+b)

(10(10+b) = (10*10) + (10*b)   – zehn mal zehn plus zehn mal b


a(10 *b) = 10*a + (a*b)  – zehn mal a plus a mal b  )


(10+a) *(10+b) = 10(10+b) + a(10+b)


(Da die Zehne den ersten drei so man aus Klammern geht,

Konnen wir machen unseren Trick als Formula steht!)




(10+a) *(10 +b) = 10x 10 + 10*a + 10*b + a*b


(10+a+b)*10 + a*b


Nimm die erste Zahl plus die letzte Ziffer von der zweiten

Hang eine Null dran (mal 10) und jetzt bist du bereitet

Wenn du das Produkt der letzten Ziffern addierst

Dann bist du fertig und du werdest schneller wenn du das noch mal probierst!


And… damit du kannst noch mal probieren…. DorFuchs made a whole video of other examples to try on his second channel, DuFrosch –

Danke schӧn DorFuchs, and I’ll definitely check out some more of your mathematical raps sometime!




Imperative forms: Because he’s telling us directly to do something, DorFuchs uses the imperative with verbs such as ‘Nimm’ and ‘Hang’ The imperative of ‘nehmen  is’nimm’ or ‘hangen’ to ‘Hang’.

Mathematical vocab: addieren – to add or – ‘plus’ +: but pronounced ‘P l UU s’ rather than English ‘p l uh ss’

multiplizieren – to multiply, or ‘mal’, to ‘times’, as in 6 times 7 = 42. Notice also ‘mal’ is used for times in other ways, such as ‘noch mal’ -I like to think of it as ‘still (another) time’

Die Zahl-(plural Die Zahlen) – number(s)

(And, just in case, eins(1), zwei(2), drei (3), vier(4), fuenf (5), sechs(6), sieben(7), acht(8), neun(9), zehn (10), elf, zwolf, dreizehn (13), vierzehn (14)… und so weiter…)

Der Ziffer – digit


(What does this have to do with PI Day? Check this out by DorFuchs- Pi ist irrational!

(I still don’t know why.)







Pokemon Translation Game- Grass type Gym (Gras Arena)

Presenting the first Gym of my Pokemon Translation Game – the Grass type gym!

Here it is! (German to English)

I also find the Scatter option cool.

And, if your typing skills are up for it, the Gravity game.

While looking at the reasons behind some of the Pokemon names, I actually found a few interesting things. I love how aspects of every story can be based on or inspired by either real things or by other stories, sometimes even ancient myths, and it seems the Pokemon franchise is no exception.

Treecko , Grovyle and Sceptile (Geckarbor, Reptain und Gewaldro)

These three tree gecko-like Pokemon are inspired by an even more interesting real life creature – a leaf-tailed gecko!
Apparently they only live in Madagascar and can climb up flat vertical surfaces without anything stick on their feet. They can do this because they have tiny hairs on the pads of their feet, that are less than a millimetre thick. On their own they can’t hold onto anything at that size, yet because there are thousands of them, they allow the leaf-tailed gecko to grip onto even the shiniest of surfaces and stick and unstick its feet to walk along them. There are many species, and these make up the genus called Uroplatus.

Treecko (German: Geckarbor) (Japanese: Kimroi)

Anyway, Treecko is the most directly inspired by the leaf-tailed gecko – it being called the Tree Gecko Pokemon. Its English name even comes from ‘tree’ and ‘gecko’. Its German name, ‘Geckarbor’, comes from similar roots, ‘Gecko’ and ‘arbor’ which means ‘tree’ in Latin.

In Japanese, this Pokemon is called Kimori. It could be a mashup of ‘ki’, meaning tree and ‘yamori’, a gecko.

Grovyle (German: Reptain) (Japanese: Juptile)

Treecko’s evolution is called Grovyle in English – this is made up of the words ‘grove’, meaning a group of trees, and the end of the word ‘reptile’. As well as the leaf-tailed gecko, Grovyle’s appearance is apparently inspired by a much older reptile -the dinosaur Dromaesaurus. This dinosaur is said to have had feathers on its body – perhaps this is similar to the leaves on Grovyle’s body.
In German it is called ‘Reptain’, from ’das Reptil’ and ‘der Hain’, meaning grove, so the inspirations of Grovyle are similar to English. (‘Hain’ or ‘Freund Hain’ is also a word for the personification of Death. Spooky… especially as the particular species of leaf-tailed gecko that Grovyle/Reptain might be based on is called Uroplatus phantasticus, also known as the satanic leaf-tailed gecko! Maybe geckoes have something to do with the underworld? Or… probably not, as the name was first applied to the species by a gecko seller who wanted them to sound cooler so he could sell more of them.)

In Japanese it is called Juptile, the prefix ‘ju’ either from the English word jungle or Japanese ‘ju’ meaning tree, and reptile.

Sceptile (German: Gewwaldro) Japanese: Jukai

The last Pokemon in this evolution chain is Sceptile. In English, the name ‘Sceptile’ could come from ‘reptile’ and a genus of plants called Sceptiridium – or a ‘sceptre’, which is something a king holds, perhaps referencing Sceptile’s power- indeed its title is ‘King of the Forest.’
In German, its name ‘Gewaldro’ could refer to ‘Gewalt’, which means violence but can also mean force or power, and ‘Wald’ the word for forest. The prefix ‘dro’ is probably from ‘drohen’, meaning to threaten. This could suggest that Scepitle’s German name ‘Gewaldro’ is more focused on its power and the fact it is a Grass type. Meanwhile, ‘Sceptile’ more references the fact it is based of a reptile, and hints at its power or its grass typing with ‘scept’.
In Japanese, Sceptile is known as ‘Jukain’, as ‘jukai’ means jungle.

Turtwig , Grotle , and Torterra (Chelast, Chelcharain and Chelterrar

The Turtwig evolution line are based on tortoises. Also, Grotle and Torterra have bushes and even part of a tree on their back. This is based off the concept that the world is held up in space by a turtle, particularly in Hinduism, but also in other myths around the word, such as Chinese legend – but the version of the World Turtle that seems to be the basis of these Pokemon is from a legend among the Native American Lepane people, in which the Creator planted a large tree that grew from the mud on a turtle’s back. The concept of the World Turtle, supporting four elephants is in Hindu mythology. It also featured in the late Terry Pratchett’s Discworld series.

Inspired by the idea of a turtle with the world on its back, the evolution line appears to show a tree growing from the shell of the Pokemon as they get bigger. Their names also reflect the stages of the tree.

Turtwig (German: Chelast) (Japanese: Naetle)

In English, Turtwig comes from the words ‘turtle’, the aforementioned creature it is based off, and ‘twig’, the small branch to be found on its head.
In German, it is called ‘Chelast’. The prefix ‘Chel’ is from the Greek word for turtle, Chelonia. This is why all Turtwig’s evolutions begin with Chel in German, although the word doesn’t come from German itself. ‘Chelast’ also involve ‘der Ast’, which is a branch. This suggests that, similarly to English, it refers to the twig on this Pokemon’s head.
In Japanese it is called ‘Naetle’, inspired by the word turtle and ‘nae’, a sprout, similar to that on Turtwig’s head; this seems to be more accurate, as the small growth isn’t yet a fully grown branch.

Grotle (German: Chelarain) (Japanese: Hayashigame)

Turtwig’s evolution is Grotle. In English, this comes from the word ‘grove’, and turtle. In German it is ‘Chelarain’ – from Chelonia, ’Carapax’, meaning ‘carapace’, which is the hard upper crust on an animal’s shell, and ‘der Hain’. Similarly to English it refers to the ‘grove’, implying that Turtwig or Chelast’s small amount of greenery has grown bigger.
In Japanese it is ‘Hayashigame’, with ‘hayashi’ meaning grove, and ‘kame’ meaning turtle. The idea of Grotle being the ‘Grove Pokemon’ that it is, appears in all three languages.

Torterra (German: Chelterrar) (Japanese: Dodaitose)

Now for the final evolution- Torterra! This large Pokemon is also a Ground type as well as a Grass type, something that’s referenced in the ‘terra’ part of its English name, which is Latin for ground. The ‘tort’ prefix could refer to a tortoise.
Its Japanese name is Dodaitose – ‘do’ means earth or ground, and ‘dai’ means large. ‘dodai’ means foundation, possible because a large area of ground is a foundation, particularly for buildings, which is perhaps where the word comes from. (Warning: I do not speak Japanese.) The tose comes from English tortoise.
The German name ‘Chelterrar’ also takes the idea of being a Ground-type tortoise to embody or support the world, like the World Tortoise does. The ‘terrar’ comes from Greek ‘terra’ like in the English name ‘Torterrra’.

Hoppip, Skipoom, and Jumpluff (Hoppspross, Hubelupf und Papungha)

For some reason, it took me a while to notice this, but the design of this evolution line of Pokemon are based on the life stages of a dandelion. Their English names also involve the idiom ‘a hop, a skip and a jump’, which often implies a short journey, ie ‘He lives just a hop, a skip and a jump away’ perhaps to suggest each can jump higher than the last as their flower grows.
In English, Hoppip comes from ‘hop and ‘pip, another name for a seed, or a high-pitched squeaking sound.
In German, Hoppip is called ‘Hoppspross’. This seems to have similar inspirations from Hoppip, with ‘hopfen’ a verb meaning to hop, and ‘der Spross’, a sprout. Hoppip’s leaves sort of look like the leaves of a dandelion, suggesting it’s sprouted but not yet grown into a flower.
In Japanese, Hoppip is ‘Hanecco’. Perhaps ironically, all the Japanese names for this evolution end in ‘necco’ ‘Nekko means root, even though these Pokemon don’t have any. They are also referencing the growth stages of the dandelion, and the pefix ‘Ha’ means leaf, referring to the leaves that make up a windmill on this Pokemon’s head.

Skiploom (Hubelupf) (Poppocco)

Next up, Skiploom. In English, ‘to skip’ is to make a small jump, or to play skipping. The ‘loom’ cloud come from ‘bloom’, meaning when a flower opens up, most likely referring to the flower on Skiploom’s head
In German, ‘Hubelupf’ is this Pokemon’s name. Just like the English version, Hubelupf references this Pokemon’s higher jump, as ‘hüpfen’ means to skip. The start of the word could be from ‘hubbelig’, bumpy.

In Japanese it is called ‘Poppoco’, from ‘tanpoppo’, dandelion, and again the prefix ‘nekko’, root.

Jumpluff (German: Papungha) (Japanese: Wattacco)

The final evolution is Jumpluff. In English this completes the pattern by referencing a ‘jump’, and the final stage of the dandelion, its ‘fluff’.
In German this Pokemon is called ‘Papungha’, something I noticed while watching my first German-dubbed Pokemon film, Pokemon 4Ever. This also refers to the full growth of the flower with ‘pappus’ , the scientific name for the bristles on a dandelion seed, and ‘sprunghaft’, an adjective meaning jumpy, implying how high this Pokemon can go. Like a real life dandelion seed, it is carried by the wind. Just like English ‘Jumpluff’ the name refers to the dandelions atop its head, and its jump when carried by the wind.

In Japanese the theme of the flower dandelion growth also reaches its climax – its name is ‘Wattaco’, with ‘watta’ meaning cotton, and the nekko referring to roots like all this Pokemon’s pre-evolutions.

Chespin Quiladin and Chesnaught (Igamaro, Igastarnish and Brigaron)

These three Pokemon, both their names and designs, are based on hegdehogs.

Chespin (Japanese: Harimaron) (German: Igamaro)

Chespin’s English name is made up of chestnut, a brown fruit with a spiky green outer shell, and pin, a sharp point. Its German name is Igamaro, from ‘der Igel’, hedgehog and Marone, the chestnut fruit.
This is similar to the Japanese inspirations – in Japanese, this Pokemon is Harimaron, made up of ‘harinezumi, meaning hedgehog (with ‘hari’ meaning pin), and Spanish for brown, marron.

Quilladin (Japanese: Hariborg) (German: Igastarnish)

The Japanese Hariborg is from harinezumi, hedgehog and bogu, armour (or bouge, French for chesnut shell). It could be either, because this Pokemon’s chestnut shell also serves as it armour.

English Quilladin is from quil, a synonym for pin, and… Aladin? Nope, it’s from the paladin, who were said to be warriors of King Charlemange of France’s court. Charlemange was also the first Holy Roman Emperor.
The German name Igastarnish is from ‘Igel’, hedgehog, Kastine, ‘ chestnut’ and ‘Harnisch’, a historical suit of armour.

<a href="; target="_blank" Rowlet (German: Bauz) (Japanese: Mokuroh)

The newest Grass type starter from the upcoming game Pokemon Sun and Moon, Rowlet is based on a small owl, hence its English name includes ,owlet’, and the ‘r’ could stand for ’round, possibly referring to its shape.

Its Japanese name was the first to be released as ‘Mokuroh’ – from ‘moku’, wood, refering to its Grass type status, and ‘fukuro’, owl.

Its German name is Bauz – from ‘der Baum’, meaning tree’ and ‘Kauz’ a family of owls called Strigadae , one of the two owl families called ‘true owls’ (the other being barn owls, more like Hedwig from Harry Potter)

There are many fan theories as to what these new starters will look like when they evolve, but nothing official has been confirmed as of yet. However, I theorize that they might involve something to do with wood, as this is involved in Rowlet’s Japanese name.

Chesnaught (Japanese: Brigaron) (German: Brigaron)

Its Japanese name is Brigarron, from brigdardine, a type of Middle Ages armour, and marron.

Chesnaught is from chestnut and dreadnought, originally the name of a battleship: the HMS Dreadnought.

Its German name is extremely similar to its Japanese name- Brigaron, from ‘die Brigantine’, meaning the brigadine armour, and Marone, chestnut.

There are others, but I think going into them would make the game too easy… besides, there’s more Gyms to create…