Babylonian numbers

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In this activity we explore the number system of the ancient Babylonians.

The ancient Babylonians used cuneiform characters to write their numbers.

What are the 2 basic ancient Babylonian numerical symbols and what do they mean?

Discuss the limitations of the Babylonian system. Then debate whether these so-called limitations were actually limitations at all.

Is the Babylonian system more of a place-value system or a concatenation system?

Fill out the following table, simplifying any calculations.

$\renewcommand {\arraystretch }{2.3} \begin{array}{| c | c || c | c || c | c |} \hline Hindu-Arabic & Cuneiform & Hindu-Arabic & Cuneiform & Hindu-Arabic & Cuneiform \\ \hline \hline 5 \times 1 & \hspace {20mm} & 5 \times 2 &\hspace {20mm} & 5 \times 3 & \hspace {20mm}\\ \hline 5 \times 4 & & 5 \times 5 & & 5 \times 6 & \\ \hline 5 \times 7 & & 5 \times 8 & & 5 \times 9 & \\ \hline 5 \times 10 & & 5 \times 20 & & 5 \times 30 & \\ \hline 5 \times 40 & & 5 \times 50 & & \frac 15 & \\ \hline \frac {1}{4} & & \frac {1}{9} & & \frac {1}{10}& \\ \hline \frac {5}{6} & & \frac {1}{20} & & \frac {1}{100} & \\ \hline \end{array}$

Use your table to make the following calculations. You should work in base sixty, though you may use Hindu-Arabic numerals.

(a): $34 \times 5$
(b): $1,47 \div 5$
(c): $2,30 \div 4$
(d): $8,6,15 \div 6,40$

2025-01-06 15:51:45

Press...	...to do
left/right arrows	Move cursor
shift+left/right arrows	Select region
ctrl+a	Select all
ctrl+x/c/v	Cut/copy/paste
ctrl+z/y	Undo/redo
ctrl+left/right	Add entry to list or column to matrix
shift+ctrl+left/right	Add copy of current entry/column to to list/matrix
ctrl+up/down	Add row to matrix
shift+ctrl+up/down	Add copy of current row to matrix
ctrl+backspace	Delete current entry in list or column in matrix
ctrl+shift+backspace	Delete current row in matrix

Type...	...to get
norm	$\|\|\blue{[?]}\|\|$
text	$\text{\blue{[?]}}$
sym_name	$\backslash\texttt{\blue{[?]}}$
abs	$\left\|\blue{[?]}\right\|$
sqrt	$\sqrt{\blue{[?]}}$
paren	$\left(\blue{[?]}\right)$
floor	$\lfloor \blue{[?]} \rfloor$
factorial	$\blue{[?]}!$
exp	${\blue{[?]}}^{\blue{[?]}}$
sub	${\blue{[?]}}_{\blue{[?]}}$
frac	$\dfrac{\blue{[?]}}{\blue{[?]}}$
int	$\displaystyle\int{\blue{[?]}}d\blue{[?]}$
defi	$\displaystyle\int_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}d\blue{[?]}$
deriv	$\displaystyle\frac{d}{d\blue{[?]}}\blue{[?]}$
sum	$\displaystyle\sum_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}$
prod	$\displaystyle\prod_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}$
root	$\sqrt[\blue{[?]}]{\blue{[?]}}$
vec	$\left\langle \blue{[?]} \right\rangle$
mat	$\left(\begin{matrix} \blue{[?]} \end{matrix}\right)$
*	$\cdot$
infinity	$\infty$
arcsin	$\arcsin\left(\blue{[?]}\right)$
arccos	$\arccos\left(\blue{[?]}\right)$
arctan	$\arctan\left(\blue{[?]}\right)$
sin	$\sin\left(\blue{[?]}\right)$
cos	$\cos\left(\blue{[?]}\right)$
tan	$\tan\left(\blue{[?]}\right)$
sec	$\sec\left(\blue{[?]}\right)$
csc	$\csc\left(\blue{[?]}\right)$
cot	$\cot\left(\blue{[?]}\right)$
log	$\log\left(\blue{[?]}\right)$
ln	$\ln\left(\blue{[?]}\right)$
alpha	$\alpha$
beta	$\beta$
gamma	$\gamma$
delta	$\delta$
epsilon	$\epsilon$
zeta	$\zeta$
eta	$\eta$
theta	$\theta$
iota	$\iota$
kappa	$\kappa$
lambda	$\lambda$
mu	$\mu$
nu	$\nu$
xi	$\xi$
omicron	$\omicron$
pi	$\pi$
rho	$\rho$
sigma	$\sigma$
tau	$\tau$
upsilon	$\upsilon$
phi	$\phi$
chi	$\chi$
psi	$\psi$
omega	$\omega$
Gamma	$\Gamma$
Delta	$\Delta$
Theta	$\Theta$
Lambda	$\Lambda$
Xi	$\Xi$
Pi	$\Pi$
Sigma	$\Sigma$
Phi	$\Phi$
Psi	$\Psi$
Omega	$\Omega$

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