THEMATHEMATICS

Carl Barks often used numbers in his stories (see The Numbers), but we tend to forget - or even overlook - that he in fact took the subject a few steps further by also using advanced mathematics from time to time. As you can see from the examples shown below Barks presented several different mathematical problems in his stories, and make no mistake - he also took the trouble to make the problems seem both plausible and convincing to the untrained eye! Not only was Barks very interested in mathematics during his school years (in fact, arithmetic was one of his favourite subjects), but he often consulted his National Geographic magazines and Encyclopedia Britannica to look for main ideas and impressive formulas that he could mould and then transfer to his stories. You may now - with or without a mathematical background - judge for yourself how well he did the job!

FC0456 Back to the Klondike

Scrooge suddenly remembers that the saloon owner Glittering Goldie some 50 years ago stole his pouch containing the equivalent of a thousand dollars from him. He never saw it again, so she was forced to give Scrooge an IOU or, as he snarled, I tear this dive apart splinter by splinter! Now he has come to collect: At compound interest for fifty years it would now amount to one billion dollars! The size of the interest rate would have been about 27.5% annually, then...

U$31 All at Sea

Barks invented the Beagle boys and he added certain numbers to their chests, which undoubtedly was easier than supplying them with individual names. By just using the digits 1, 6, and 7 in a double function (for example 176-176) he would end up with 36 combinations which should be sufficient for his purpose.
Well, in this story 176-176 was portrayed two times in the same panel(!) - but maybe he was a split personality, anyway...

U$57 The Swamp of No Return

A scientist has invented an apparatus that can completely change the personality of any living being. In this panel Barks offers these impressive ingredients on differential equations from the wonderful world of mathematics.
NB.: Barks made a minor spelling error in the dialogue: Quadrantic should read Quadratic.

WDCS136 'Bridge Building'

The nephews (as Junior Woodchucks) solve a simple trigonometry problem (well, simple if you know how, of course!). They have to bridge a gully and for that end they have to know the exact distance across the stream. Using their JW protractor and some calculations they soon figure out that the distance to be 23 feet.

FC1095 The Bear Tamer

Little Helper invents a bear repellent in order to subdue a ferocious bear that almost finished off Gyro Gearloose and Gladstone Gander. In the panel Barks shows a chemistry formula:
I just stole that out of the Encyclopedia Britannica. It was a big article on chemistry with all different chemical formulas, and it was written in this gibberish - CO H and so on - and I just looked at a whole string of those things and looked at about the middle of that. And I thought, Well, may be it's harmless enough if I just take these bunch of chemicals and sort of jumble them up and stick them on a piece of paper. Well, that is what I did, and it turned out that it was a powerful chemical formula.
Indeed it was! Inadvertently Barks had come across a small part of a formula that was considered a top military secret of the USA at the time!

WDCS195 'Train Collision'

Barks presents us with two calculus problems that are both solved by the nephews. At first, they play on the floor with their toy trains; they try to figure out the precise speed of two locomotives in order to prevent them from colliding on the track. Later on the gruesome reality sets in when a TV announcer prompts people for help; a runaway locomotive and The Limited, a passenger train, are on collision course and the rescue people need to know exactly where the collision will take place. He offers a number of details: The Limited's speed uphill is 60 mph less ice slippage of 8.64%! Headwinds of 50 mph will be met for 12 miles below Blue Canyon! At mile 23 the grade increases 4% ...
Information continues to pour out enabling the nephews to calculate the point of collision, the rescuers can throw down rubber mattresses onto the track, and lives are saved!

U$69 The Cattle King

The nephews succeed in saving a high-speed train from colliding with a trainload of explosives. One of the nephews says: According to the Junior Woodchucks' Guidebook's page of differential equations in problematic variables for diminishing ratios... - His scared brother hurries him: Get to the point! And the equation follows as seen in the panel.

FC0495 'The Horseradish Story'

Scrooge points out Donald's calculus error in a very concrete and heavy-handed manner; he batters poor Donald who misreads the depth gauge as 3,000 fathoms. Scrooge - who is diving at the time - immediately realizes that this figure is equivalent to three and a quarter mile, which cannot be right. Donald soon learns that A fathom is not an inch - it's six feet.

FC0422 The Gilded Man

Barks also presents a Donald Duck one-pager in this comic book in which Donald has a riding stable. His price list proves to be a bit rash which the visiting Scrooge immediately discovers: One horse $1.00 per hour; two horses 90 cents per hour each! Three horses 80 cents per hour each! Four horses 70...
Scrooge ponders the simple mathematical problem and rents 11 horses whereupon he rides off free of charge! One can only wonder why he failed to rent more horses. That way he could have earned money on the deal...

U$13 Land Beneath the Ground

Scrooge forces Donald to accompany him underground by presenting an old IOU of his: ...for fifty cents you borrowed in 1950! At compound interest that now amounts to 500 dollars! That constitutes a whopping 115% per year! Blackmail has always been a powerful weapon....
Also, Scrooge has always swindled Donald in their working relationships by giving him less than starvation wages. Still, Donald accepts the raw deals - he knows that he is up against a magician in mathematics!

WDCS272 Spare that Hair

Donald is an expert barber who takes on all sorts of requests. One comes from an insecure young man who wants to be an egghead in order to impress his girlfriend. By simply applying a huge build-up dome of plastic foam and ivory enamel to the man's scalp he completely changes personality: All of a sudden I understand barycentric calculus and the interpolation of isoperimetric arcs! F(x) = dx = Dy + 2z!

U$59 North of the Yukon

The sleezy moneylender Soapy Slick finds an IOU from Scrooge: Here it is - the IOU he gave me in 1898! One hundred per cent interest per month, compounded forever! That means the sum doubled every month for sixty-seven years! Whee! Billions! Trillions! Uncountable fantasticatillions!
More precisely the total amount in dollars after 67 years would be a mind-boggling 243-digit figure!

CHALLENGE

U$24 The Twenty-four Carat Moon

We are often presented to figures describing the wealth of Scrooge. The incomprehensible and invented figures are always changing (see HERE), but a few times we are in fact presented to an understanding of just how much valuables Scrooge possesses.
Take for example the golden moon in U$24 The Twenty-four Carat Moon, in which he acquires a moon made totally from gold and with a diameter of 500 miles! Scrooge immediately begins to calculate its worth in gold: That much gold in dollars would be two hundred and seventy-seven untouchabatillions, six hundred and six uncomprehendabalillions... and so forth.
But in this instant - neglecting Barks' intelligent figure names - we would be able to make a more prosaic and truthful approach to the moon's actual worth: With a given diameter of 500 miles we could calculate the total volume, compare it to the weight of 24 carat gold and multiply it with the actual gold price for that time. Would take some time, though, but it can be done. Still, the value would obviously just be a fraction of Scrooge's total wealth, because it is assumed that he has most of it safely tucked away on planet Earth...

But here is a real challenge for you:

In one story Barks in fact told us exactly how much money (in normal dollars) Scrooge owns!!! You just have to look between the lines. It happened in FC0291 The Magic Hourglass, in which Scrooge is followed by bad financial luck: I can't go on like this - losing a billion dollars a minute! I'll be broke in 600 years! - Aha! There you have it black on white; Scrooge can afford to lose a cool billion a minute for the next 600 years before he runs out of cash. How much money does he have now, then???

This is a simple, straightforward calculation but the editor of this site lays down his weapons (and pencil), because he does not possess the truckloads of sheets of paper necessary to scribble down the gigantic rows of digits required. Now, is there a mathematics buff amongst the readers who dares take up the task, so that we can finally get to know the true magnitude of Scrooge's wealth ....?