Pythagorean Triples

pythagorean_triples.Rmd

---
title: "Pythagorean Triples"
author: "Edward Visel"
output:
    html_document:
        df_print: paged
---

```{r}
library(tidyverse)

legs <- function(P, c){
    discriminant <- sqrt(c^2 + 2*P*c - P^2)
    a <- (P - c - discriminant) / 2
    b <- P - c - a
    data.frame(a, b, c, P)
}

triples <- map_df(12:50000, function(P){
    c <- seq.int(from = ceiling((sqrt(2) - 1) * P),    # 45-45-90
                 to = floor((P - 1) / 2),    # flat
                 by = 1L)
    discriminant <- sqrt(c^2 + 2*P*c - P^2)
    a <- (P - c - discriminant) / 2
    is_triple <- a %% 1 == 0
    if (any(is_triple)) {
        a <- a[is_triple]
        c <- c[is_triple]
        b <- P - c - a
        list(P = rep(P, length(a)), 
             a = a, 
             b = b, 
             c = c)
    } else NULL
})
```

```{r}
plot_triples <- function(aes, ylab = deparse(aes$y), max_c = 20500){
    triples %>% 
        filter(c < max_c) %>% 
        mutate(a_parity = ifelse(a %% 2 == 0, 'even', 'odd')) %>% 
        ggplot(aes) + 
        geom_point(size = 0.5, alpha = 0.5) + 
        scale_x_continuous(labels = scales::comma_format(), expand = c(0, 0)) + 
        scale_y_continuous(labels = scales::comma_format(), expand = c(0, 0)) + 
        viridis::scale_color_viridis(
            begin = 0.3, end = 0.9, option = 'viridis', discrete = TRUE, 
            guide = guide_legend(override.aes = list(alpha = 1))) + 
        labs(title = 'Pythagorean Triples', 
             y = ylab, 
             color = expression(Parity~of~italic(a))) + 
        hrbrthemes::theme_ipsum_rc(plot_margin = margin(10, 10, 5, 10), 
                                   grid = FALSE) + 
        theme(legend.position = 'bottom', 
              legend.direction = 'horizontal', 
              legend.key.size = unit(10, 'pt'),
              legend.justification = 0.01,
              legend.margin = margin(0, 0, 0, 0),
              legend.title = element_text(size = 10),
              axis.title.y = element_text(angle = 0))
}
```

```{r}
plot_triples(aes(c, a/c, color = a_parity), ylab = expression(over(a, c)))
```

```{r}
plot_triples(aes(b, a, color = a_parity))
```

```{r}
plot_triples(aes(c, a, color = a_parity))
```