Tag Archives: deutsch

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

Image result for dorfuchs multiplizieren

(Image from YouTube)

Video: https://www.youtube.com/watch?v=EqWZGjskZUk

…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 – https://www.youtube.com/watch?v=CCdwcdCunD0

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.)






Mein Woerterbuch

.word-gender-masc {
color: blue;

.word-gender-fem {

.word-gender-neut {

.nom {col




The Word Book – otherwise known by us English speakers as – the dictionary! Here it is.

   Das deutsche-englische Worterbuch

This is a work in progress. I’m going to mark every:

  • tense
  • word gender ( masculine , feminine , or neutral )
  • case ( nominative, accusative, <span class="dat" dativ and <span class="gen" genitive)
  • <
    , I mark this with colours, but also with HTML classes to be picked up by your screen reader if you're a screen reader user.


    Edit: this isn't working…yet….



When Interests Collide: Howards Ehrengedächtnis – Goethe

Plaques created by local children (and a few adults) during an arts workshop inspired by the English Heritage Blue Plaque scheme that took place at the Tottenham Ploughman “CloudFest” 2014.

Blue plaques in a fluffy cotton cloud – made by the children and adults around the old house of Luke Howard, the classifier of the clouds. From the Tottenham Clouds website.

Luke Howard, classifier of the clouds. 28 November 1772 – 21 March 1864

Johann Wolfgang von Goethe (1749-1832), the celebrated German author and poet, was interested in clouds himself and wanted to learn more about the young Luke Howard. https://tottenhamclouds.org.uk/goethe/

Wie geht es, Leute?

So I’ve been searching around in the older forums I used to visit, and one of these is The Cloud Appreciation Society.

Not that long ago I was really interested in clouds, and they remain amongst my other interests to this day. I learnt about the different types of clouds through chatting with other people on the Society, looking at the photo they shared, and reading much more knowledge people than me attempt to identify the different types.

There are different types of cloud, and each type is given a Latin name -There had been other cloud classification systems, yet this one in Latin, the (‘educated’) ‘global language’ of the 16th century, allowed other scientists and meteorologists from around the world to also identify the cloud type.

There are many types of cloud, but the main types are:

Stratus (Latin for layer) – the lowest cloud, forming like layers of fog in a way. (In German- Sichtwolken – ‘layer clouds)

Image result for stratus clouds

Cumulus (Latin for heap) – can be found at medium height, the typical ‘candyfloss’ or ‘sheeplike’ clouds – with many different subtypes. (German: Haufenwolken or Kumulus.)

(Comes from the same Latin root as the English verb ‘accumulate’, to add on- like cumulus clouds growing bigger and more puffy)

Image result for cumulus clouds

Nimbus (Latin for ‘dark cloud’) – a prefix used for a rain cloud, typically the stratonimbus or the Cumulonimbus- the large rain cloud that may also bring thunderstorms.

Image result for cumulus clouds

(Cumulonimubs cloud – Photo by Kevin Knupp University of Illilois Cloud Catalog. Its the highest cloud and stretches its ‘plume’ above the other cumulus.)

Cirrus (Latin for a curling ringlet of hair)- the highest clouds, looking like wisps of hair, made of ice streak that streak across the stratosphere. (German: die Federwolken – ‘feather clouds)

Image result for cirrus clouds

So what does this have to do with German? Well, a good while after that, I discovered that the person who invented this Latin naming system for the clouds was called Luke Howard. He was a chemist living in 16th century East London, however he was fascinated with the clouds. I found that he had moved to Tottenham, the area where I’m from (link goes to another external article I wrote about another famous Tottenham landmark).

Luke Howard actually lived specifically in this house:

Image result for Luke Howard's house 7 bruce grove

(Caption- Luke Howard’s house in Tottenham, London, with a blue plaque on it.)

(Caption: Luke Howard’s blue plague reads: English Heritage. Luke Howard, 1772-1864, Namer Of Clouds, lived and died here.)

Luke Howard, classifier of the clouds. 28 November 1772 – 21 March 1864

The English Heritage organisation awards the Blue Plaque to mark where a famous historical person used to live. Here is a link to their website on the blue plaque. The fact that they recognised Luke Howard was amazing, however the building is old and needs to be regenerated. There is even a petition to call on developers to help save Luke Howard’s house. (link to Tottenham Clouds, another cloud-loving blog that aims to popularise the fact that the Namer of the Clouds came from its hometown.)

So that was a pretty amazing find, but what does this have to do with German? Well, then I found out that Goethe, yes Johann Wolfgang von Goethe, the famous German author and poet who wrote Die Leiden des Jungen Werthers and Dr Faustus, also wrote a poem for Luke Howard.

It’s called Howards Ehrengedachtnis, roughly translating as Howard’s honoured Memory. It was written in 1821 when Luke Howard was around 49

An article in German about it (http://bib.gfz-potsdam.de/pub/schule/goethe/startgoe1.html)

And I just had to bring all my interests full circle and translate Howards Ehrengedachtnis… So, I did.

(This is a work in progress. If you see a mistake or want to help out, leave a comment below.)

(Diese Übersetzung ist in Arbiet. Wenn Ihr einen Fehler merkt, oder Hilfe bieten wollt, posten Sie unten in die Kommentare!)

Credit to zeno.org, where I found the full poem.

Howards Ehrengedächtnis – by Johann Wolfgang von Goethe, 1821

[551] Wenn Gottheit Camarupa, hoch und hehr,

Durch Lüfte schwankend wandelt leicht und schwer,

Des Schleiers Falten sammelt, sie zerstreut,

Am Wechsel der Gestalten sich erfreut,

Jetzt starr sich hält, dann schwindet wie ein Traum,

Da staunen wir und traun dem Auge kaum;

When the god Campura, up and down,

Changes fluctuating through the air softly and violently

Of the veil’s folds collects, disperses them

In the changes of forms delights

Now rigid it holds, then disappears like a dream

Then we marvel and hardly believe our eyes.

Nun regt sich kühn des eignen Bildens Kraft,

Die Unbestimmtes zu Bestimmtem schafft;

Da droht ein Leu, dort wogt ein Elefant,

Kameles Hals, zum Drachen umgewandt,

Ein Heer zieht an, doch triumphiert es nicht,

Da es die Macht am steilen Felsen bricht;

Der treuste Wolkenbote selbst zerstiebt,

Eh er die Fern erreicht, wohin man liebt.

Now it boldly moves the picture’s own power

The uncertain established into certain

There threatens a lion, there weighed an elephant.

A camel’s neck transforms into a dragon,

An army is drawn, but not triumphantly

Because the power breaks between steep cliffs

The most trusted cloud message is itself scattered.

Until it reaches the faraway land, where we live.

Er aber, Howard, gibt mit reinem Sinn

Uns neuer Lehre herrlichsten Gewinn.

Was sich nicht halten, nicht erreichen läßt,

Er faßt es an, er hält zuerst es fest;

Bestimmt das Unbestimmte, schränkt es ein,

Benennt es treffend! – Sei die Ehre dein! –

Wie Streife steigt, sich ballt, zerflattert, fällt,

Erinnre dankbar deiner sich die Welt.

He, however, Howard, gives us with clear sense

New lessons of the most wonderful yield.

What doesn’t keep itself , can’t be achieved.

He tackles it, he first grasps the thought.

Ascertains the uncertain, narrows it down,

Names it aptly – Be the honour yours!

Like the patrol climbs, balls up, flattens, fallt,

I remember you thankfully the world


Wenn von dem stillen Wasserspiegelplan

Ein Nebel hebt den flachen Teppich an,

Der Mond, dem Wallen des Erscheins vereint,

Als ein Gespenst Gespenster bildend scheint,

Dann sind wir alle, das gestehn wir nur,

Erquickt’, erfreute Kinder, o Natur!

Related image

When from the still water mirror plan,

A fog wisp lifts from the surface of the pond.

The moon combines with the undulations of the appearance?

Like a phantom seemingly ghostly forming.

Then are we all, we all only admit,

Refreshed, delighted children – O, Nature!

Dann hebt sich’s wohl am Berge, sammelnd breit

An Streife Streifen, so umdüstert’s weit

Die Mittelhöhe, beidem gleich geneigt,

Ob’s fallend wässert oder luftig steigt.

Then lifts itself up to the mountains, accumulating wide,

Stripes are on patrol, so it () far

The middle heights, however that way inclined,

Whether it falls as water or to the air will rise.


Und wenn darauf zu höhrer Atmosphäre

Der tüchtige Gehalt berufen wäre,

Steht Wolke hoch, zum herrlichsten geballt,

Verkündet, festgebildet, Machtgewalt

Und, was ihr fürchtet und auch wohl erlebt,

Wie’s oben drohet, so es unten bebt.

Image result for cumulonimbus raining

And when to  the higher atmosphere

The capable content is called

The clouds stand high, wonderfully balled,

Announced, established, forceful might.

And, what you fear and also experience,

As it threatens over, so under it quakes.


Doch immer höher steigt der edle Drang!

Erlösung ist ein himmlisch leichter Zwang.

Ein Aufgehäuftes, flockig löst sich’s auf,

Wie Schäflein tripplend, leicht gekämmt zu Hauf.

So fließt zuletzt, was unten leicht entstand,

Dem Vater oben still in Schoß und Hand.

Image result for cirrus clouds

But ever higher climbs the noble urge.

Redemption is a celestial lighter force.

A lumpy accumulation, itself flakily resolves

Like scurrying lambs, combed lightly to a heap.

So it flows finally, what below easily occurs.

To the Father still above in shot and hand.

[552] Nimbus

Nun laßt auch niederwärts, durch Erdgewalt

Herabgezogen, was sich hoch geballt,

In Donnerwettern wütend sich ergehn,

Heerscharen gleich entrollen und verwehn! –

Der Erde tätig-leidendes Geschick!

Doch mit dem Bilde hebet euren Blick:

Die Rede geht herab, denn sie beschreibt,

Der Geist will aufwärts, wo er ewig bleibt.

Image result

Now let also downwards, through the earth’s force.

Be pulled down, what was on high.

In thunderstorms, angrily they fare,

Legions unroll themselves and blow away!

The Earth-active and Earth-suffering skill

But with the pictures you all lift your gaze.

There is talk of this, because it is described,

The spirit wants to go upwards, where he forever stays.

Image result for cirrus clouds diagram

Things I’ll do in my Blog of Things


A History Story

Random German Word of the Day (with Wordbox and 10-min-made story)
Wahloses deutsches Wort des Tages (mit Wortkiste und kurz geschaften Gesichste)

Translating my earlier stories (Pasour downwards ?)
Meine frueher Gesichten ubersetzen

Enthusing about history, linguistics, German and writing (more connected than anyone might think)

Links coming soon