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Copy file name to clipboardExpand all lines: lectures/french_rev.md
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extension: .md
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format_name: myst
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format_version: 0.13
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jupytext_version: 1.16.2
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jupytext_version: 1.16.7
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kernelspec:
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display_name: Python 3 (ipykernel)
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language: python
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but were substantially less than government expenditures during wars
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* In France, even in peace time, tax revenues were substantially less than government expenditures
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```{code-cell} ipython3
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---
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mystnb:
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figure:
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caption: "Military Spending in Britain and France"
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caption: Military Spending in Britain and France
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name: fr_fig4
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---
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# Read the data from Excel file
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A remarkable aspect of figure {numref}`fr_fig4` is that despite having a population less than half of France's, Britain was able to finance military expenses of about the same amounts as France's.
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This testifies to Britain's having created state institutions that could sustain high tax collections, government spending , and government borrowing. See {cite}`north1989`.
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This testifies to Britain's having created state institutions that could sustain high tax collections, government spending , and government borrowing. See {cite}`north1989`.
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```{code-cell} ipython3
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---
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mystnb:
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figure:
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caption: "Government Expenditures and Tax Revenues in Britain"
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caption: Government Expenditures and Tax Revenues in Britain
Figures {numref}`fr_fig2` and {numref}`fr_fig3` summarize British and French government fiscal policies during the century before the start of the French Revolution in 1789.
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mystnb:
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figure:
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caption: "Ratio of debt service to taxes, Britain and France"
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caption: Ratio of debt service to taxes, Britain and France
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But as we'll see in our next graph, on the eve of the French Revolution in 1788, the fiscal *law of gravity* that worked so well in Britain did not working very well in France.
Copy file name to clipboardExpand all lines: lectures/greek_square.md
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fascinating passage:
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```{epigraph}
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The square root of 2, which was the first irrational to be discovered, was known to the early Pythagoreans, and ingenious methods of approximating to its value were discovered. The best was as follows: Form two columns of numbers, which we will call the $a$'s and the $b$'s; each starts with a $1$. The next $a$, at each stage, is formed by adding the last $a$ and the $b$ already obtained; the next $b$ is formed by adding twice the previous $a$ to the previous $b$. The first 6 pairs so obtained are $(1,1), (2,3), (5,7), (12,17), (29,41), (70,99)$. In each pair, $2 a - b$ is $1$ or $-1$. Thus $b/a$ is nearly the square root of two, and at each fresh step it gets nearer. For instance, the reader may satisy himself that the square of $99/70$ is very nearly equal to $2$.
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The square root of 2, which was the first irrational to be discovered, was known to the early Pythagoreans, and ingenious methods of approximating to its value were discovered. The best was as follows: Form two columns of numbers, which we will call the $a$'s and the $b$'s; each starts with a $1$. The next $a$, at each stage, is formed by adding the last $a$ and the $b$ already obtained; the next $b$ is formed by adding twice the previous $a$ to the previous $b$. The first 6 pairs so obtained are $(1,1), (2,3), (5,7), (12,17), (29,41), (70,99)$. In each pair, $2 a^2 - b^2$ is $1$ or $-1$. Thus $b/a$ is nearly the square root of two, and at each fresh step it gets nearer. For instance, the reader may satisy himself that the square of $99/70$ is very nearly equal to $2$.
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```
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This lecture drills down and studies this ancient method for computing square roots by using some of the matrix algebra that we've learned in earlier quantecon lectures.
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